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Kac, Victor G.

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Author ID: kac.victor-g Recent zbMATH articles by "Kac, Victor G."
Published as: Gatti, V.; Kac, V.; Kac, V. G.; Kac, Victor; Kac, Victor G.; Kats, V. G.
Homepage: http://www-math.mit.edu/~kac/
External Links: MGP · Math-Net.Ru · Wikidata · GND
Documents Indexed: 257 Publications since 1967, including 16 Books
Biographic References: 1 Publication
all top 5

Co-Authors

58 single-authored
37 De Sole, Alberto
26 Wakimoto, Minoru
16 Möseneder Frajria, Pierluigi
16 Papi, Paolo
16 Valeri, Daniele
11 Peterson, Dale Harvey
10 Bakalov, Bojko
10 van de Leur, Johan W.
9 Cantarini, Nicoletta
8 De Concini, Corrado
7 Cheng, Shun-Jen
7 Liberati, Jose I.
6 Adamović, Dražen
6 Boyallian, Carina
6 Perše, Ozren
5 Carpentier, Sylvain
5 Elashvili, Alexander G.
5 Gorelik, Maria
5 Rudakov, Alexei Nikolaevich
5 Vinberg, Èrnest Borisovich
4 D’Andrea, Alessandro
4 Procesi, Claudio
4 Radul, Andrey
4 Weisfeiler, Boris
3 Heluani, Reimundo
3 Kazhdan, David A.
3 Novikov, Sergeĭ Petrovich
3 Wang, Weiqiang
3 Zel’manov, Efim Isaakovich
2 Arbarello, Enrico
2 Bokut, Leonid A.
2 Fattori, Davide
2 Frenkel, Edward V.
2 Gabber, Ofer
2 Jakobsen, Hans Plesner
2 Jibladze, Mamuka A.
2 Kang, Seok-Jin
2 Parshin, Alexei N.
2 Platonov, Vladimir Petrovich
2 Popov, Vladimir Leonidovich
2 Raina, Ashok K.
2 Retakh, Alexander
2 Rozhkovskaya, Natasha
2 Shestakov, Ivan Pavlovich
2 Smilga, Andrei V.
2 Taimanov, Iskander Asanovich
2 Todorov, Ivan T.
2 Turhan, Refik
2 Xu, Feng
2 Yan, Catherine Huafei
1 Astashov, A. M.
1 Astashova, Irina V.
1 Barakat, Aliaa
1 Beck, Jonathan
1 Bocharov, Alexei V.
1 Brylinski, Jean-Luc
1 Brylinski, Ranee Kathryn
1 Bukhshtaber, Viktor Matveevich
1 Caselli, Fabrizio
1 Cellini, Paola
1 Chetverikov, Vladimir N.
1 Cheung, Pokman
1 Dadok, Jiri
1 Deodhar, Vinay V.
1 Dong, Chongying
1 Frenkel, Igor B.
1 Fuchs, Dmitry Borisovich
1 Futorny, Vyacheslav M.
1 Gardini, Matteo
1 Golenishcheva-Kutuzova, Maria I.
1 Golod, Evgeniĭ Solomonovich
1 Grigorchuk, Rostislav Ivanovich
1 Guillemin, Victor W.
1 Hekmati, Pedram
1 Helemskii, Alexander Ya.
1 Hogben, Leslie
1 Kashuba, Iryna
1 Kemer, Aleksandr Robertovich
1 Kharchenko, Vladislav K.
1 Kharlampovich, Olga G.
1 Khor’kova, Nina Grigor’evna
1 Kolesnikov, Pavel Sergeevich
1 Kosmann-Schwarzbach, Yvette
1 Krasil’shchik, Iosif Semënovich
1 Krichever, Igor’ Moiseevich
1 Krishchenko, Alexander P.
1 Kutateladze, Semën Samsonovich
1 Kyrychenko, Volodymyr Vasyl’ovych
1 Lando, Sergei K.
1 Latyshev, Viktor Nikolaevich
1 Lau, Michael W.
1 Lepowsky, James
1 Longo, Roberto
1 Lychagin, Valentin V.
1 Makar-Limanov, Leonid G.
1 Mal’tsev, Yuriĭ Nikolaevich
1 Manin, Yuri Ivanovich
1 Margulis, Grigoriĭ Aleksandrovich
1 Martínez López, Consuelo
1 Marvan, Michal
...and 38 more Co-Authors
all top 5

Serials

33 Communications in Mathematical Physics
28 Advances in Mathematics
15 Journal of Mathematical Physics
10 IMRN. International Mathematics Research Notices
10 Japanese Journal of Mathematics. 3rd Series
9 Transformation Groups
7 Journal of Algebra
5 Functional Analysis and its Applications
5 Proceedings of the National Academy of Sciences of the United States of America
5 Selecta Mathematica. New Series
4 Uspekhi Matematicheskikh Nauk [N. S.]
4 Inventiones Mathematicae
4 Mathematics of the USSR. Izvestiya
4 Bulletin of the American Mathematical Society. New Series
3 Communications in Algebra
3 Russian Mathematical Surveys
3 Comptes Rendus. Mathématique. Académie des Sciences, Paris
3 Advanced Series in Mathematical Physics
3 Progress in Mathematics
2 Letters in Mathematical Physics
2 Bulgarian Journal of Physics
2 Journal of the American Mathematical Society
2 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya
2 Advances in Theoretical and Mathematical Physics
2 Moscow Mathematical Journal
2 Journal of Algebra and its Applications
2 University Lecture Series
1 International Journal of Modern Physics A
1 Mathematical Notes
1 Nuclear Physics. B
1 Physics Letters. B
1 Annales de l’Institut Fourier
1 Canadian Mathematical Bulletin
1 Journal of Functional Analysis
1 Memoirs of the American Mathematical Society
1 Transactions of the Moscow Mathematical Society
1 Acta Applicandae Mathematicae
1 Advances in Mathematics
1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
1 Russian Academy of Sciences. Izvestiya. Mathematics
1 Journal of Lie Theory
1 Izvestiya: Mathematics
1 Resenhas do Instituto do Matemática e Estatística da Universidade de São Paulo
1 The Asian Journal of Mathematics
1 Journal of the European Mathematical Society (JEMS)
1 Communications in Contemporary Mathematics
1 International Journal of Geometric Methods in Modern Physics
1 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A
1 Contemporary Mathematics
1 Mathematical Sciences Research Institute Publications
1 Nederlandse Akademie van Wetenschappen. Proceedings. Series A. Indagationes Mathematicae
1 Springer Proceedings in Mathematics & Statistics
1 Transactions of A. Razmadze Mathematical Institute
1 Universitext

Publications by Year

Citations contained in zbMATH

230 Publications have been cited 10,546 times in 6,071 Documents Cited by Year
Infinite dimensional Lie algebras. 3rd ed. Zbl 0716.17022
Kac, Victor G.
1990
Lie superalgebras. Zbl 0366.17012
Kac, V. G.
961
1977
Quantum calculus. Zbl 0986.05001
Kac, Victor; Cheung, Pokman
487
2002
Vertex algebras for beginners. 2nd ed. Zbl 0924.17023
Kac, Victor
261
1998
Bombay lectures on highest weight representations of infinite dimensional Lie algebras. Zbl 0668.17012
Kac, V. G.; Raina, A. K.
251
1987
Infinite dimensional Lie algebras. An introduction. Zbl 0537.17001
Kac, Victor G.
241
1983
Basic representations of affine Lie algebras and dual resonance models. Zbl 0493.17010
Frenkel, I. B.; Kac, V. G.
232
1980
Infinite-dimensional Lie algebras, theta functions and modular forms. Zbl 0584.17007
Kac, Victor G.; Peterson, Dale H.
214
1984
Infinite dimensional Lie algebras. 2nd ed. Zbl 0574.17010
Kac, Victor G.
208
1985
Contravariant form for infinite-dimensional Lie algebras and superalgebras. Zbl 0574.17002
Kac, V. G.
206
1979
Highest weight representations of infinite-dimensional Lie algebras. Zbl 0425.17009
Kac, V. G.
181
1980
Infinite root systems, representations of graphs and invariant theory. Zbl 0427.17001
Kac, V. G.
155
1980
Vertex algebras for beginners. Zbl 0861.17017
Kac, Victor
153
1996
A sketch of Lie superalgebra theory. Zbl 0359.17009
Kac, V. G.
126
1977
Some remarks on nilpotent orbits. Zbl 0431.17007
Kac, V. G.
124
1980
Structure of representations with highest weight of infinite-dimensional Lie algebras. Zbl 0427.17011
Kac, V. G.; Kazhdan, D. A.
124
1979
Representations of quantum groups at roots of 1. Zbl 0738.17008
De Concini, Corrado; Kac, Victor G.
123
1990
Infinite flag varieties and conjugacy theorems. Zbl 0512.17008
Peterson, Dale H.; Kac, Victor G.
114
1983
Infinite-dimensional algebras, Dedekind’s \(\eta\)-function, classical Möbius function and the very strange formula. Zbl 0391.17010
Kac, V. G.
111
1978
Simple irreducible graded Lie algebras of finite growth. Zbl 0222.17007
Kac, V. G.
106
1970
Spin and wedge representations of infinite-dimensional Lie algebras and groups. Zbl 0469.22016
Kac, Victor G.; Peterson, Dale H.
105
1981
Modular invariant representations of infinite-dimensional Lie algebras and superalgebras. Zbl 0652.17010
Kac, Victor G.; Wakimoto, Minoru
104
1988
Modular and conformal invariance constraints in representation theory of affine algebras. Zbl 0661.17016
Kac, Victor G.; Wakimoto, Minoru
97
1988
Classification of simple Z-graded Lie superalgebras and simple Jordan superalgebras. Zbl 0367.17007
Kac, V. G.
95
1977
Integrable highest weight modules over affine superalgebras and number theory. Zbl 0854.17028
Kac, Victor G.; Wakimoto, Minoru
94
1994
Structure theory of finite conformal algebras. Zbl 0918.17019
D’Andrea, Alessandro; Kac, Victor G.
90
1998
Characters of typical representations of classical Lie superalgebras. Zbl 0359.17010
Kac, V. G.
90
1977
Moduli spaces of curves and representation theory. Zbl 0647.17010
Arbarello, E.; De Concini, C.; Kac, V. G.; Procesi, C.
89
1988
Quasifinite highest weight modules over the Lie algebra of differential operators on the circle. Zbl 0826.17027
Kac, Victor; Radul, Andrey
87
1993
Finite vs affine \(W\)-algebras. Zbl 1161.17015
De Sole, Alberto; Kac, Victor G.
82
2006
\({\mathcal W}_{1+\infty}\) and \({\mathcal W}(gl_ N)\) with central charge \(N\). Zbl 0838.17028
Frenkel, Edward; Kac, Victor; Radul, Andrey; Wang, Weiqiang
79
1995
Quantum reduction for affine superalgebras. Zbl 1106.17026
Kac, Victor; Roan, Shi-Shyr; Wakimoto, Minoru
78
2003
Classification of infinite-dimensional simple linearly compact Lie superalgebras. Zbl 0929.17026
Kac, Victor G.
78
1998
Infinite root systems, representations of graphs and invariant theory. II. Zbl 0497.17007
Kac, V. G.
78
1982
Cohomology of conformal algebras. Zbl 0959.17018
Bakalov, Bojko; Kac, Victor G.; Voronov, Alexander A.
72
1999
Characters and fusion rules for \(W\)-algebras via quantized Drinfeld- Sokolov reduction. Zbl 0768.17008
Frenkel, Edward; Kac, Victor; Wakimoto, Minoru
71
1992
Integrable highest weight modules over affine superalgebras and Appell’s function. Zbl 0980.17002
Kac, Victor G.; Wakimoto, Minoru
68
2001
Quantum reduction and representation theory of superconformal algebras. Zbl 1049.17025
Kac, Victor G.; Wakimoto, Minoru
67
2004
Realization of the basic representations of the Euclidean Lie algebras. Zbl 0476.17003
Kac, V. G.; Kazhdan, D. A.; Lepowsky, J.; Wilson, R. L.
66
1981
Theory of finite pseudoalgebras. Zbl 1001.16021
Bakalov, Bojko; D’Andrea, Alessandro; Kac, Victor G.
64
2001
Field algebras. Zbl 1032.17045
Bakalov, Bojko; Kac, Victor G.
63
2003
Representations of classical Lie superalgebras. Zbl 0388.17002
Kac, V.
63
1978
A new class of unitarizable highest weight representations of infinite dimensional Lie algebras. Zbl 0581.17009
Jakobsen, H. P.; Kac, V. G.
61
1985
Conformal modules. Zbl 1022.17018
Cheng, Shun-Jen; Kac, Victor G.
60
1997
Representation theory of the vertex algebra \(W_{1+\infty}\). Zbl 0862.17023
Kac, Victor; Radul, Andrey
57
1996
On integral representations of \(q\)-gamma and \(q\)-beta functions. Zbl 1225.33017
De Sole, Alberto; Kac, Victor G.
54
2005
Poisson vertex algebras in the theory of Hamiltonian equations. Zbl 1244.17017
Barakat, Aliaa; De Sole, Alberto; Kac, Victor G.
53
2009
Quantum coadjoint action. Zbl 0747.17018
De Concini, C.; Kac, V. G.; Procesi, C.
52
1992
Laplace operators of infinite-dimensional Lie algebras and theta functions. Zbl 0532.17008
Kac, Victor G.
52
1984
Infinite-dimensional Lie algebras and Dedekind’s \(\eta\)-function. Zbl 0299.17005
Kac, V. G.
51
1974
Structure of some categories of representations of infinite-dimensional Lie algebras. Zbl 0491.17008
Deodhar, Vinay V.; Gabber, Ofer; Kac, Victor
50
1982
Classification of modular invariant representations of affine algebras. Zbl 0742.17022
Kac, V. G.; Wakimoto, M.
47
1989
Coadjoint action of a semisimple algebraic group and the center of the enveloping algebra in characteristic \(p\). Zbl 0324.17001
Kac, V.; Weisfeiler, Boris
47
1976
The \(n\)-component KP hierarchy and representation theory. Zbl 1062.37071
Kac, V. G.; van de Leur, J. W.
45
2003
Vertex operator superalgebras and their representations. Zbl 0838.17035
Kac, Victor; Wang, Weiqiang
45
1994
Automorphisms of finite order of semisimple Lie algebras. Zbl 0274.17002
Kac, V. G.
44
1969
Superconformal current algebras and their unitary representations. Zbl 0599.17011
Kac, Victor G.; Todorov, Ivan T.
43
1985
Quasifinite representations of classical Lie subalgebras of \({\mathcal W}_{1+\infty}\). Zbl 0938.17018
Kac, Victor G.; Wang, Weiqiang; Yan, Catherine H.
41
1998
On defining relations of certain infinite-dimensional Lie algebras. Zbl 0474.17007
Gabber, Ofer; Kac, Victor G.
41
1981
Classification of finite simple Lie conformal superalgebras. Zbl 1050.17023
Fattori, Davide; Kac, Victor G.
39
2002
Some quantum analogues of solvable Lie groups. Zbl 0878.17014
De Concini, C.; Kac, V. G.; Procesi, C.
39
1995
The \(n\)-component KP hierarchy and representation theory. Zbl 0843.35105
Kac, V. G.; van de Leur, J. W.
38
1993
Polar representations. Zbl 0611.22009
Dadok, Jiri; Kac, Victor
38
1985
Classification of good gradings of simple Lie algebras. Zbl 1073.17002
Elashvili, A. G.; Kac, V. G.
37
2005
Description of filtered Lie algebras with which graded Lie algebras of Cartan type are associated. Zbl 0317.17002
Kac, V. G.
37
1975
Irreducible representations of Lie \(p\)-algebras. Zbl 0237.17003
Weisfeiler, B. Yu.; Kac, V. G.
37
1971
Defining relations of certain infinite dimensional groups. Zbl 0625.22014
Kac, V. G.; Peterson, D. H.
36
1985
Formal distribution algebras and conformal algebras. Zbl 1253.17002
Kac, Victor G.
35
1999
A new \(N=6\) superconformal algebra. Zbl 0906.17020
Cheng, Shun-Jen; Kac, Victor G.
35
1997
On classification of superconformal algebras. Zbl 0938.17500
Kac, V. G.; van de Leur, J. W.
33
1989
An elucidation of ”Infinite-dimensional algebras…and the very strange formula.” \(E^{(1)}_8\) and the cube root of the modular invariant j. Zbl 0431.17009
Kac, V. G.
31
1980
Bombay lectures on highest weight representations of infinite dimensional Lie algebras. 2nd ed. Zbl 1294.17021
Kac, Victor G.; Raina, Ashok K.; Rozhkovskaya, Natasha
30
2013
Classification of linearly compact simple Jordan and generalized Poisson superalgebras. Zbl 1173.17023
Cantarini, Nicoletta; Kac, Victor G.
30
2007
Solitons in affine and permutation orbifolds. Zbl 1078.81051
Kac, Victor G.; Longo, Roberto; Xu, Feng
28
2005
Vacuum structure in supersymmetric Yang-Mills theories with any gauge group. Zbl 1035.81061
Kac, V. G.; Smilga, A. V.
28
2000
Exceptional hierarchies of soliton equations. Zbl 0691.17014
Kac, Victor G.; Wakimoto, Minoru
28
1989
Finite linear groups whose ring of invariants is a complete intersection. Zbl 0483.14002
Kac, Victor; Watanabe, Kei-Ichi
28
1982
Affine Lie algebras and Hecke modular forms. Zbl 0457.17007
Kac, V. G.; Peterson, D. H.
28
1980
Quasi-homogeneous cones. Zbl 0163.16902
Vinberg, È. B.; Kac, V. G.
28
1967
Non-local Poisson structures and applications to the theory of integrable systems. Zbl 1286.37062
De Sole, Alberto; Kac, Victor G.
27
2013
On automorphisms of Kac-Moody algebras and groups. Zbl 0851.17026
Kac, V. G.; Wang, S. P.
27
1992
Some remarkable degenerations of quantum groups. Zbl 0795.17006
De Concini, C.; Kac, V. G.; Procesi, C.
26
1993
\(\Gamma\)-conformal algebras. Zbl 1031.81527
Golenishcheva-Kutuzova, Maria I.; Kac, Victor G.
25
1998
Branching functions for winding subalgebras and tensor products. Zbl 0717.17017
Kac, V. G.; Wakimoto, M.
25
1990
The infinite wedge representation and the reciprocity law for algebraic curves. Zbl 0699.22028
Arbarello, E.; De Concini, C.; Kac, V. G.
25
1989
112 constructions of the basic representation of the loop group of \(E_ 8\). Zbl 0642.17013
Kac, Victor G.; Peterson, Dale H.
25
1985
Sur les groupes linéaires algébriques dont l’algèbre des invariants est libre. Zbl 0343.20023
Kac, Victor G.; Popov, Vladimir L.; Vinberg, Ernest B.
25
1976
Classical \(\mathcal W\)-algebras and generalized Drinfeld-Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebras. Zbl 1320.37031
De Sole, Alberto; Kac, Victor G.; Valeri, Daniele
24
2013
Classification of simple linearly compact \(n\)-Lie superalgebras. Zbl 1232.17008
Cantarini, Nicoletta; Kac, Victor G.
24
2010
On simplicity of vacuum modules. Zbl 1112.17023
Gorelik, Maria; Kac, Victor
24
2007
Unitary structure in representations of infinite-dimensional groups and a convexity theorem. Zbl 0534.17008
Kac, V. G.; Peterson, D. H.
24
1984
On the classification of subalgebras of \(\text{Cend}_N\) and \(\text{gc}_N\). Zbl 1034.17018
Boyallian, Carina; Kac, Victor G.; Liberati, Jose I.
23
2003
Affine orbifolds and rational conformal field theory extensions of \(W_{1+\infty}\). Zbl 0904.17021
Kac, Victor G.; Todorov, Ivan T.
23
1997
Torsion in cohomology of compact Lie groups and Chow rings of reductive algebraic groups. Zbl 0566.57028
Kac, V. G.
23
1985
A new class of unitarizable highest weight representations of infinite- dimensional Lie algebras. II. Zbl 0688.17007
Jakobsen, Hans Plesner; Kac, Victor
22
1989
Super boson-fermion correspondence. Zbl 0625.58041
Kac, V. G.; van de Leur, J.
22
1987
Regular functions on certain infinite-dimensional groups. Zbl 0578.17014
Kac, Victor G.; Peterson, Dale H.
22
1983
On rationality of \(W\)-algebras. Zbl 1221.17033
Kac, Victor G.; Wakimoto, Minoru
21
2008
Twisted modules over lattice vertex algebras. Zbl 1229.17028
Bakalov, Bojko; Kac, Victor G.
20
2005
Spinors of 13-dimensional space. Zbl 0429.20043
Gatti, V.; Viniberghi, E.
20
1978
Computation of cohomology of Lie conformal and Poisson vertex algebras. Zbl 07229490
Bakalov, Bojko; De Sole, Alberto; Kac, Victor G.
1
2020
An operadic approach to vertex algebra and Poisson vertex algebra cohomology. Zbl 07107328
Bakalov, Bojko; De Sole, Alberto; Heluani, Reimundo; Kac, Victor G.
3
2019
Local and non-local multiplicative Poisson vertex algebras and differential-difference equations. Zbl 1421.35323
De Sole, Alberto; Kac, Victor G.; Valeri, Daniele; Wakimoto, Minoru
3
2019
Polynomial tau-functions of BKP and DKP hierarchies. Zbl 1421.37028
Kac, Victor; Van De Leur, Johan
2
2019
On Dynkin gradings in simple Lie algebras. Zbl 1436.17039
Elashvili, Alexander; Jibladze, Mamuka; Kac, Victor
1
2019
Kostant pairs of Lie type and conformal embeddings. Zbl 07215802
Adamović, Dražen; Kac, Victor G.; Möseneder Frajria, Pierluigi; Papi, Paolo; Perše, Ozren
1
2019
Trace functions of the parafermion vertex operator algebras. Zbl 07055753
Dong, Chongying; Kac, Victor; Ren, Li
1
2019
Classical affine \(\mathcal W\)-algebras and the associated integrable Hamiltonian hierarchies for classical Lie algebras. Zbl 1426.17015
De Sole, Alberto; Kac, Victor G.; Valeri, Daniele
8
2018
Conformal embeddings of affine vertex algebras in minimal \(W\)-algebras. I: Structural results. Zbl 1420.17028
Adamović, Dražen; Kac, Victor G.; Möseneder Frajria, Pierluigi; Papi, Paolo; Perše, Ozren
7
2018
Equivalence of formulations of the MKP hierarchy and its polynomial tau-functions. Zbl 1401.14209
Kac, Victor G.; van de Leur, Johan W.
6
2018
Finite \(W\)-algebras for \(\mathfrak{gl}_N\). Zbl 1398.17007
De Sole, Alberto; Kac, Victor G.; Valeri, Daniele
6
2018
A Lax type operator for quantum finite \(W\)-algebras. Zbl 06976969
De Sole, Alberto; Kac, Victor G.; Valeri, Daniele
3
2018
On the classification of non-equal rank affine conformal embeddings and applications. Zbl 1447.17018
Adamović, Dražen; Kac, Victor G.; Möseneder Frajria, Pierluigi; Papi, Paolo; Perše, Ozren
2
2018
On characters of irreducible highest weight modules of negative integer level over affine Lie algebras. Zbl 07065401
Kac, Victor G.; Wakimoto, Minoru
1
2018
A remark on boundary level admissible representations. Zbl 1418.17054
Kac, Victor G.; Wakimoto, Minoru
10
2017
Conformal embeddings of affine vertex algebras in minimal \(W\)-algebras. II: Decompositions. Zbl 1425.17037
Adamović, Dražen; Kac, Victor G.; Möseneder Frajria, Pierluigi; Papi, Paolo; Perše, Ozren
7
2017
Introduction to vertex algebras, Poisson vertex algebras, and integrable Hamiltonian PDE. Zbl 1430.17088
Kac, Victor
2
2017
Representations of superconformal algebras and mock theta functions. Zbl 1436.17034
Kac, V. G.; Wakimoto, M.
1
2017
Structure of classical (finite and affine) \(\mathcal W\)-algebras. Zbl 1395.17063
De Sole, Alberto; Kac, Victor G.; Valeri, Daniele
13
2016
A new scheme of integrability for (bi)Hamiltonian PDE. Zbl 1393.17048
De Sole, Alberto; Kac, Victor G.; Valeri, Daniele
12
2016
Classical affine \(\mathcal{W}\)-algebras for \(\mathfrak{gl}_N\) and associated integrable Hamiltonian hierarchies. Zbl 1433.17038
De Sole, Alberto; Kac, Victor G.; Valeri, Daniele
12
2016
Finite vs. infinite decompositions in conformal embeddings. Zbl 1405.17049
Adamović, Dražen; Kac, Victor G.; Möseneder Frajria, Pierluigi; Papi, Paolo; Perše, Ozren
8
2016
Representations of affine superalgebras and mock theta functions. II. Zbl 1372.17020
Kac, Victor G.; Wakimoto, Minoru
7
2016
Representations of affine superalgebras and mock theta functions. III. Zbl 1373.17027
Kac, Victor G.; Wakimoto, Minoru
5
2016
Classification of linearly compact simple Nambu-Poisson algebras. Zbl 1386.17025
Cantarini, Nicoletta; Kac, Victor G.
1
2016
Adler-Gelfand-Dickey approach to classical \(\mathcal{W}\)-algebras within the theory of Poisson vertex algebras. Zbl 1327.17024
De Sole, Alberto; Kac, Victor G.; Valeri, Daniele
15
2015
Conformal embeddings and simple current extensions. Zbl 1418.17059
Kac, Victor G.; Möseneder Frajria, Pierluigi; Papi, Paolo; Xu, Feng
12
2015
Characters of (relatively) integrable modules over affine Lie superalgebras. Zbl 1378.17017
Gorelik, Maria; Kac, Victor G.
9
2015
Double Poisson vertex algebras and non-commutative Hamiltonian equations. Zbl 1327.17023
De Sole, Alberto; Kac, Victor G.; Valeri, Daniele
7
2015
Singular degree of a rational matrix pseudodifferential operator. Zbl 1338.12006
Carpentier, Sylvain; De Sole, Alberto; Kac, Victor G.
5
2015
Erratum to: “Classical \(\mathcal W\)-algebras and generalized Drinfeld-Sokolov hierarchies for minimal and short nilpotents”. Zbl 1327.17022
De Sole, Alberto; Kac, Victor G.; Valeri, Daniele
5
2015
On integrability of some bi-Hamiltonian two field systems of partial differential equations. Zbl 1321.37068
De Sole, Alberto; Kac, Victor G.; Turhan, Refik
4
2015
Representations of affine superalgebras and mock theta functions. Zbl 1372.17019
Kac, Victor G.; Wakimoto, Minoru
13
2014
Dirac reduction for Poisson vertex algebras. Zbl 1368.17031
De Sole, Alberto; Kac, Victor G.; Valeri, Daniele
10
2014
Classical \(\mathcal{W}\)-algebras and generalized Drinfeld-Sokolov hierarchies for minimal and short nilpotents. Zbl 1327.17021
De Sole, Alberto; Kac, Victor G.; Valeri, Daniele
9
2014
Rational matrix pseudodifferential operators. Zbl 1321.35269
Carpentier, Sylvain; De Sole, Alberto; Kac, Victor G.
8
2014
A new approach to the Lenard-Magri scheme of integrability. Zbl 1305.37035
De Sole, Alberto; Kac, Victor G.; Turhan, Refik
4
2014
Dirac operators and the very strange formula for Lie superalgebras. Zbl 1344.17010
Kac, Victor G.; Möseneder Frajria, Pierluigi; Papi, Paolo
3
2014
Integrability of Dirac reduced bi-Hamiltonian equations. Zbl 1326.35310
De Sole, Alberto; Kac, Victor G.; Valeri, Daniele
2
2014
Algebraic vs physical \(N = 6\) 3-algebras. Zbl 1288.81134
Cantarini, Nicoletta; Kac, Victor G.
1
2014
Bombay lectures on highest weight representations of infinite dimensional Lie algebras. 2nd ed. Zbl 1294.17021
Kac, Victor G.; Raina, Ashok K.; Rozhkovskaya, Natasha
30
2013
Non-local Poisson structures and applications to the theory of integrable systems. Zbl 1286.37062
De Sole, Alberto; Kac, Victor G.
27
2013
Classical \(\mathcal W\)-algebras and generalized Drinfeld-Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebras. Zbl 1320.37031
De Sole, Alberto; Kac, Victor G.; Valeri, Daniele
24
2013
The variational Poisson cohomology. Zbl 1290.17027
De Sole, Alberto; Kac, Victor G.
14
2013
Classification of finite irreducible modules over the Lie conformal superalgebra \(CK_{6}\). Zbl 1280.17010
Boyallian, Carina; Kac, Victor G.; Liberati, José I.
10
2013
Some remarks on non-commutative principal ideal rings. Zbl 1270.12002
Carpentier, Sylvain; De Sole, Alberto; Kac, Victor G.
6
2013
Cyclic elements in semisimple Lie algebras. Zbl 1329.17007
Elashvili, A. G.; Kac, V. G.; Vinberg, E. B.
5
2013
Irreducible modules over finite simple Lie pseudoalgebras. II: Primitive pseudoalgebras of type \(K\). Zbl 1287.17051
Bakalov, Bojko; D’Andrea, Alessandro; Kac, Victor G.
2
2013
Some algebraic properties of differential operators. Zbl 06234829
Carpentier, Sylvain; De Sole, Alberto; Kac, Victor G.
8
2012
Essential variational Poisson cohomology. Zbl 1297.17012
De Sole, Alberto; Kac, Victor G.
7
2012
Denominator identities for finite-dimensional Lie superalgebras and Howe duality for compact dual pairs. Zbl 1335.17004
Gorelik, Maria; Kac, Victor G.; Möseneder Frajria, Pierluigi; Papi, Paolo
3
2012
On complete reducibility for infinite-dimensional Lie algebras. Zbl 1225.17026
Gorelik, Maria; Kac, Victor
7
2011
Classification of linearly compact simple algebraic \(N=6\) 3-algebras. Zbl 1270.17002
Cantarini, Nicoletta; Kac, Victor G.
6
2011
Calculus structure on the Lie conformal algebra complex and the variational complex. Zbl 1317.18019
De Sole, Alberto; Hekmati, Pedram; Kac, Victor G.
3
2011
Classification of simple linearly compact \(n\)-Lie superalgebras. Zbl 1232.17008
Cantarini, Nicoletta; Kac, Victor G.
24
2010
Classification of linearly compact simple rigid superalgebras. Zbl 1269.17002
Cantarini, Nicoletta; Kac, Victor G.
13
2010
On classification of Poisson vertex algebras. Zbl 1235.17020
De Sole, Alberto; Kac, Victor G.; Wakimoto, Minoru
7
2010
Irreducible modules over finite simple Lie conformal superalgebras of type \(K\). Zbl 1311.17005
Boyallian, Carina; Kac, Victor G.; Liberati, José I.
6
2010
Denominator formulas for Lie superalgebras (extended abstract). Zbl 1373.17013
Kac, Victor; Möseneder Frajria, Pierluigi; Papi, Paolo
2
2010
Poisson vertex algebras in the theory of Hamiltonian equations. Zbl 1244.17017
Barakat, Aliaa; De Sole, Alberto; Kac, Victor G.
53
2009
Lie conformal algebra cohomology and the variational complex. Zbl 1225.49009
De Sole, Alberto; Kac, Victor G.
17
2009
On exceptional nilpotents in semisimple Lie algebras. Zbl 1252.17006
Elashvili, A. G.; Kac, V. G.; Vinberg, E. B.
3
2009
Differential conformal superalgebras and their forms. Zbl 1217.17018
Kac, Victor; Lau, Michael; Pianzola, Arturo
3
2009
On rationality of \(W\)-algebras. Zbl 1221.17033
Kac, Victor G.; Wakimoto, Minoru
21
2008
Multiplets of representations, twisted Dirac operators and Vogan’s conjecture in affine setting. Zbl 1177.17016
Kac, Victor G.; Möseneder Frajria, Pierluigi; Papi, Paolo
6
2008
SUSY lattice vertex algebras. Zbl 1202.81151
Heluani, Reimundo; Kac, Victor G.
2
2008
On the kernel of the affine Dirac operator. Zbl 1162.17024
Kac, Victor G.; Möseneder Frajria, Pierluigi; Papi, Paolo
2
2008
Simple Jordan conformal superalgebras. Zbl 1236.17040
Kac, Victor G.; Retakh, Alexander
1
2008
Classification of linearly compact simple Jordan and generalized Poisson superalgebras. Zbl 1173.17023
Cantarini, Nicoletta; Kac, Victor G.
30
2007
On simplicity of vacuum modules. Zbl 1112.17023
Gorelik, Maria; Kac, Victor
24
2007
Supersymmetric vertex algebras. Zbl 1205.17029
Heluani, Reimundo; Kac, Victor G.
13
2007
Characters of highest weight modules over affine Lie algebras are meromorphic functions. Zbl 1152.17011
Gorelik, Maria; Kac, Victor
1
2007
Finite vs affine \(W\)-algebras. Zbl 1161.17015
De Sole, Alberto; Kac, Victor G.
82
2006
Representations of simple finite Lie conformal superalgebras of type \(W\) and \(S\). Zbl 1111.17001
Boyallian, Carina; Kac, Victor G.; Liberati, Jose I.; Rudakov, Alexei
10
2006
Infinite-dimensional primitive linearly compact Lie superalgebras. Zbl 1204.17017
Cantarini, Nicoletta; Kac, Victor G.
10
2006
Irreducible modules over finite simple Lie pseudoalgebras. I: Primitive pseudoalgebras of type \(W\) and \(S\). Zbl 1104.17006
Bakalov, Bojko; D’Andrea, Alessandro; Kac, Victor G.
10
2006
Generalized vertex algebras. Zbl 1241.17029
Bakalov, B.; Kac, V. G.
7
2006
Automorphisms and forms of simple infinite-dimensional linearly compact Lie superalgebras. Zbl 1115.17009
Cantarini, Nicoletta; Kac, Victor G.
6
2006
Decomposition rules for conformal pairs associated to symmetric spaces and Abelian subalgebras of \(\mathbb Z_{2}\)-graded Lie algebras. Zbl 1162.17022
Cellini, Paola; Kac, Victor G.; Möseneder Frajria, Pierluigi; Papi, Paolo
6
2006
On integral representations of \(q\)-gamma and \(q\)-beta functions. Zbl 1225.33017
De Sole, Alberto; Kac, Victor G.
54
2005
Classification of good gradings of simple Lie algebras. Zbl 1073.17002
Elashvili, A. G.; Kac, V. G.
37
2005
Solitons in affine and permutation orbifolds. Zbl 1078.81051
Kac, Victor G.; Longo, Roberto; Xu, Feng
28
2005
Twisted modules over lattice vertex algebras. Zbl 1229.17028
Bakalov, Bojko; Kac, Victor G.
20
2005
Freely generated vertex algebras and nonlinear Lie conformal algebras. Zbl 1104.17016
De Sole, Alberto; Kac, Victor G.
14
2005
Structure theory of finite Lie conformal superalgebras. Zbl 1229.17027
Fattori, Davide; Kac, Victor G.; Retakh, Alexander
12
2005
Quantum reduction in the twisted case. Zbl 1132.17306
Kac, Victor G.; Wakimoto, Minoru
11
2005
Quantum reduction and representation theory of superconformal algebras. Zbl 1049.17025
Kac, Victor G.; Wakimoto, Minoru
67
2004
Addendum: Generalized Spencer cohomology and filtered deformations of \(\mathbb Z\)-graded Lie superalgebras. Zbl 1094.17005
Cheng, Shun-Jen; Kac, Victor
6
2004
Representations of the exceptional Lie superalgebra \(E(3,6)\). III: Classification of singular vectors. Zbl 1063.17004
Kac, Victor G.; Rudakov, Alexei
2
2004
Nonlinear Lie conformal algebras. Zbl 1161.17320
Kac, Victor
1
2004
Quantum reduction for affine superalgebras. Zbl 1106.17026
Kac, Victor; Roan, Shi-Shyr; Wakimoto, Minoru
78
2003
Field algebras. Zbl 1032.17045
Bakalov, Bojko; Kac, Victor G.
63
2003
The \(n\)-component KP hierarchy and representation theory. Zbl 1062.37071
Kac, V. G.; van de Leur, J. W.
45
2003
On the classification of subalgebras of \(\text{Cend}_N\) and \(\text{gc}_N\). Zbl 1034.17018
Boyallian, Carina; Kac, Victor G.; Liberati, Jose I.
23
2003
Finite growth representations of infinite Lie conformal algebras. Zbl 1061.17007
Boyallian, Carina; Kac, Victor G.; Liberati, Jose I.
10
2003
Quantum calculus. Zbl 0986.05001
Kac, Victor; Cheung, Pokman
487
2002
Classification of finite simple Lie conformal superalgebras. Zbl 1050.17023
Fattori, Davide; Kac, Victor G.
39
2002
Classification of supersymmetries. Zbl 1057.17021
Kac, Victor G.
14
2002
Subalgebras of \(\text{gc}_N\) and Jacobi polynomials. Zbl 1037.17025
De Sole, Alberto; Kac, Victor G.
11
2002
Representations of the exceptional Lie superalgebra \(E(3,6)\). I: Degeneracy conditions. Zbl 0997.17005
Kac, Victor G.; Rudakov, Alexei
9
2002
...and 130 more Documents
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Cited by 4,576 Authors

126 Kac, Victor G.
66 Su, Yucai
45 Li, Haisheng
39 Zhao, Kaiming
37 Dong, Chongying
36 Creutzig, Thomas
36 Jing, Naihuan
36 Zhang, Ruibin
33 Van der Jeugt, Joris
32 De Sole, Alberto
32 Milas, Antun
32 Zhang, Yongzheng
31 Tan, Shao Bin
30 Arakawa, Tomoyuki
30 Liu, Wende
30 Misra, Kailash C.
30 Serganova, Vera V.
29 Adamović, Dražen
29 Feĭgin, Boris L’vovich
28 Kang, Seok-Jin
27 Jiang, Cuipo
27 Ntouyas, Sotiris K.
27 Okado, Masato
27 Shu, Bin
26 Futorny, Vyacheslav M.
26 Linshaw, Andrew Ross
26 Tariboon, Jessada
25 Frenkel, Edward V.
25 Kwon, Jae-Hoon
25 Lam, Ching Hung
25 van de Leur, Johan W.
23 Chari, Vyjayanthi
23 Chen, Liangyun
23 Naito, Satoshi
23 Pianzola, Arturo
23 Ridout, David
22 Cheng, Shun-Jen
22 Kolesnikov, Pavel Sergeevich
22 Palev, Tchavdar D.
22 Wang, Weiqiang
21 Elduque, Alberto
21 Gould, Mark D.
21 Liu, Dong
20 Bringmann, Kathrin
20 Eswara Rao, Senapathi
20 Kashiwara, Masaki
20 Papi, Paolo
20 Valeri, Daniele
19 Lepowsky, James
19 Stoilova, Nedjalka I.
18 Agrawal, Purshottam Narain
18 Boyallian, Carina
18 Gao, Yun
18 Gupta, Vijay
18 Leites, Dimitry A.
18 Palmkvist, Jakob
18 Pei, Yufeng
18 Yakimov, Milen T.
17 Kaĭgorodov, Ivan B.
17 Kleinschmidt, Axel
17 Liberati, Jose I.
17 Schilling, Anne
16 Fuchs, Jürgen
16 Guo, Xiangqian
16 Hu, Naihong
16 Jimbo, Michio
16 Lü, Rencai
16 Miwa, Tetsuji
16 Poletaeva, Elena
16 Wakimoto, Minoru
16 Xu, Feng
16 Xu, Xiaoping
15 Benkart, Georgia M.
15 Brundan, Jonathan
15 Gannon, Terry
15 Geer, Nathan
15 Halpern, Martin B.
15 Kuniba, Atsuo
15 Morita, Jun
15 Möseneder Frajria, Pierluigi
15 Nicolai, Hermann
15 Oh, Se-jin
15 Patureau-Mirand, Bertrand
15 Reshetikhin, Nikolai Yu.
15 Sun, Jiancai
15 Yamane, Hiroyuki
15 Yao, Yufeng
15 Zel’manov, Efim Isaakovich
15 Zhang, Yaozhong
14 Bakalov, Bojko
14 Billig, Yuly
14 Chen, Hongjia
14 Hong, Yanyong
14 Mursaleen, Mohammad
14 Penkov, Ivan B.
14 Ren, Li
14 Sagaki, Daisuke
14 Vasserot, Eric
14 Viswanath, Sankaran
14 Xia, Chunguang
...and 4,476 more Authors
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Cited in 386 Serials

730 Journal of Algebra
400 Communications in Mathematical Physics
378 Journal of Mathematical Physics
285 Advances in Mathematics
247 Communications in Algebra
239 Nuclear Physics. B
199 Journal of High Energy Physics
163 Journal of Pure and Applied Algebra
157 Letters in Mathematical Physics
133 Transactions of the American Mathematical Society
112 Journal of Geometry and Physics
79 Proceedings of the American Mathematical Society
76 Transformation Groups
68 Theoretical and Mathematical Physics
68 Mathematische Zeitschrift
67 Algebras and Representation Theory
66 Duke Mathematical Journal
65 Inventiones Mathematicae
58 Journal of Algebra and its Applications
55 Functional Analysis and its Applications
53 Representation Theory
53 Advances in Difference Equations
50 Selecta Mathematica. New Series
46 Mathematische Annalen
43 Annales de l’Institut Fourier
39 International Journal of Modern Physics A
37 Publications of the Research Institute for Mathematical Sciences, Kyoto University
36 Applied Mathematics and Computation
36 Journal of Algebraic Combinatorics
35 Linear Algebra and its Applications
35 Journal of Mathematical Sciences (New York)
33 Physics Letters. B
33 Proceedings of the Japan Academy. Series A
33 Abstract and Applied Analysis
31 Acta Mathematica Sinica. English Series
30 Frontiers of Mathematics in China
29 Compositio Mathematica
29 Algebra Colloquium
29 Journal of Nonlinear Mathematical Physics
27 Journal of Functional Analysis
26 Journal of the American Mathematical Society
26 International Journal of Mathematics
25 Israel Journal of Mathematics
25 Journal of Mathematical Analysis and Applications
24 Communications in Contemporary Mathematics
23 Journal of Combinatorial Theory. Series A
22 Physics Letters. A
22 Science China. Mathematics
21 Linear and Multilinear Algebra
21 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
20 Reports on Mathematical Physics
20 Journal of Soviet Mathematics
20 Bulletin of the American Mathematical Society. New Series
20 Annals of Mathematics. Second Series
19 Journal of Inequalities and Applications
18 Reviews in Mathematical Physics
18 Manuscripta Mathematica
18 Acta Applicandae Mathematicae
18 Journal of Physics A: Mathematical and Theoretical
17 Nuclear Physics, B, Proceedings Supplements
16 Journal of Computational and Applied Mathematics
16 Science in China. Series A
16 The Ramanujan Journal
15 Physica D
15 Advances in Mathematical Physics
13 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
13 Comptes Rendus. Mathématique. Académie des Sciences, Paris
13 Central European Journal of Mathematics
13 Japanese Journal of Mathematics. 3rd Series
12 Computers & Mathematics with Applications
12 International Journal of Theoretical Physics
12 Chinese Annals of Mathematics. Series B
12 Annals of Physics
12 Journal of the European Mathematical Society (JEMS)
12 Annales Henri Poincaré
12 Research in the Mathematical Sciences
11 Algebra and Logic
11 Geometriae Dedicata
11 Nagoya Mathematical Journal
11 Siberian Mathematical Journal
11 Indagationes Mathematicae. New Series
11 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
11 Mediterranean Journal of Mathematics
10 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
10 Journal für die Reine und Angewandte Mathematik
10 Proceedings of the London Mathematical Society. Third Series
10 Transactions of the Moscow Mathematical Society
10 Advances in Applied Mathematics
9 Rocky Mountain Journal of Mathematics
9 Chaos, Solitons and Fractals
9 Memoirs of the American Mathematical Society
9 St. Petersburg Mathematical Journal
9 Journal of Lie Theory
9 Bulletin des Sciences Mathématiques
9 International Journal of Geometric Methods in Modern Physics
9 Proceedings of the Steklov Institute of Mathematics
8 Modern Physics Letters A
8 Journal of Statistical Physics
8 Journal of the Mathematical Society of Japan
8 Journal of Symbolic Computation
...and 286 more Serials
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Cited in 59 Fields

3,816 Nonassociative rings and algebras (17-XX)
1,486 Quantum theory (81-XX)
634 Associative rings and algebras (16-XX)
579 Group theory and generalizations (20-XX)
574 Algebraic geometry (14-XX)
431 Topological groups, Lie groups (22-XX)
406 Combinatorics (05-XX)
356 Dynamical systems and ergodic theory (37-XX)
299 Number theory (11-XX)
268 Partial differential equations (35-XX)
232 Differential geometry (53-XX)
218 Global analysis, analysis on manifolds (58-XX)
191 Special functions (33-XX)
177 Relativity and gravitational theory (83-XX)
166 Difference and functional equations (39-XX)
160 Ordinary differential equations (34-XX)
159 Commutative algebra (13-XX)
152 Statistical mechanics, structure of matter (82-XX)
136 Manifolds and cell complexes (57-XX)
128 Category theory; homological algebra (18-XX)
128 Approximations and expansions (41-XX)
114 Linear and multilinear algebra; matrix theory (15-XX)
105 Functional analysis (46-XX)
89 Several complex variables and analytic spaces (32-XX)
78 Real functions (26-XX)
51 Operator theory (47-XX)
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45 Functions of a complex variable (30-XX)
44 \(K\)-theory (19-XX)
43 Algebraic topology (55-XX)
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18 Order, lattices, ordered algebraic structures (06-XX)
17 Integral transforms, operational calculus (44-XX)
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14 Field theory and polynomials (12-XX)
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3 Optics, electromagnetic theory (78-XX)
3 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
2 General topology (54-XX)
1 Potential theory (31-XX)

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