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Skrypnyk, Taras Volodymyrovych

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Author ID: skrypnyk.taras-v Recent zbMATH articles by "Skrypnyk, Taras Volodymyrovych"
Published as: Scrypnik, T. V.; Skrypnik, T.; Skrypnik, T. V.; Skrypnyk, T.; Skrypnyk, T. V.; Skrypnyk, Taras; Skrypnyk, Taras V.
External Links: Math-Net.Ru
Documents Indexed: 82 Publications since 1996

Publications by Year

Citations contained in zbMATH

53 Publications have been cited 227 times in 78 Documents Cited by Year
Generalized Gaudin systems in a magnetic field and non-skew-symmetric \(r\)-matrices. Zbl 1127.81023
Skrypnyk, T.
20
2007
Integrable quantum spin chains, non-skew symmetric \(r\)-matrices and quasigraded Lie algebras. Zbl 1101.81064
Skrypnyk, T.
20
2006
Quantum integrable systems, non-skew-symmetric \(r\)-matrices and algebraic Bethe ansatz. Zbl 1121.81068
Skrypnyk, T.
12
2007
“\(Z_2\)-graded” Gaudin models and analytical Bethe ansatz. Zbl 1262.81064
Skrypnyk, T.
11
2013
Generalized Gaudin spin chains, nonskew symmetric \(r\)-matrices, and reflection equation algebras. Zbl 1153.81435
Skrypnyk, Taras
10
2007
Quasigraded deformations of loop algebras and classical integrable systems. Zbl 1047.37052
Skrypnyk, T.
10
2002
Quasigraded Lie algebras on hyperelliptic curves and classical integrable systems. Zbl 1032.17052
Skrypnyk, T.
8
2001
Generalized shift elements and classical \(r\)-matrices: construction and applications. Zbl 1303.37028
Skrypnyk, T.
7
2014
Integrability and superintegrability of the generalized \(n\)-level many-mode Jaynes-Cummings and Dicke models. Zbl 1283.81084
Skrypnyk, T.
7
2009
Generalized quantum Gaudin spin chains, involutive automorphisms and “twisted” classical \(r\)-matrices. Zbl 1111.81087
Skrypnyk, T.
7
2006
Deformations of loop algebras and integrable systems: hierarchies of integrable equations. Zbl 1064.37055
Skrypnyk, T.
7
2004
Infinite-dimensional Lie algebras, classical \(r\)-matrices, and Lax operators: two approaches. Zbl 1328.17020
Skrypnyk, T.
6
2013
Generalized \(n\)-level Jaynes-Cummings and Dicke models, classical rational \(r\)-matrices and algebraic Bethe ansatz. Zbl 1153.81020
Skrypnyk, T.
6
2008
Separation of variables for linear Lax algebras and classical \(r\)-matrices. Zbl 1403.37067
Dubrovin, B.; Skrypnyk, T.
5
2018
Lie algebras with triangular decompositions, non-skew-symmetric classical \(r\)-matrices and Gaudin-type integrable systems. Zbl 1185.81095
Skrypnyk, T.
5
2010
Non-skew-symmetric classical \(r\)-matrices, algebraic Bethe ansatz, and Bardeen-Cooper-Schrieffer-type integrable systems. Zbl 1202.17016
Skrypnyk, T.
5
2009
New integrable Gaudin-type systems, classical \(r\)-matrices and quasigraded Lie algebras. Zbl 1123.81369
Skrypnyk, T.
5
2005
Quantum integrable models of interacting bosons and classical \(r\)-matrices with spectral parameters. Zbl 1326.81280
Skrypnyk, T.
4
2015
Integrable modifications of Dicke and Jaynes-Cummings models, Bose-Hubbard dimers and classical \(r\)-matrices. Zbl 1189.81290
Skrypnyk, T.
4
2010
Non-skew-symmetric classical \(r\)-matrices and integrable cases of the reduced BCS model. Zbl 1181.81063
Skrypnyk, T.
4
2009
Special quasigraded Lie algebras and integrable Hamiltonian systems. Zbl 1218.37103
Skrypnyk, T.
4
2007
General integrable \(n\)-level, many-mode Janes-Cummings-Dicke models and classical \(r\)-matrices with spectral parameters. Zbl 1315.81114
Skrypnyk, T.
3
2015
Quasi-periodic functions on the torus and \(sl(n)\)-elliptic Lie algebra. Zbl 1274.22012
Skrypnyk, T.
3
2012
Elliptic three-boson system, “two-level three-mode” JCD-type models and non-skew-symmetric classical r-matrices. Zbl 1246.82027
Skrypnyk, T.
3
2012
Compatible Poisson brackets, quadratic Poisson algebras and classical \(r\)-matrices. Zbl 1180.37106
Roubtsov, V.; Skrypnyk, T.
3
2009
Dual \(R\)-matrix integrability. Zbl 1182.37037
Skrypnyk, T. V.
3
2008
New non-skew symmetric classical \(r\)-matrices and ‘twisted’ quasigraded Lie algebras. Zbl 1108.37047
Skrypnyk, T.
3
2007
Modified non-Abelian Toda field equations and twisted quasigraded Lie algebras. Zbl 1112.37073
Skrypnyk, T.
3
2006
‘Doubled’ generalized Landau-Lifshitz hierarchies and special quasigraded Lie algebras. Zbl 1063.22025
Skrypnyk, T.
3
2004
Hierarchies of integrable equations associated with hyperelliptic Lie algebras. Zbl 1001.37075
Skrypnyk, T.; Holod, P.
3
2001
Singular orbits of the co-adjoint representation of Euclidean groups. Zbl 0964.22018
Boyarskij, A. M.; Skrypnik, T. V.
3
2000
Separation of variables for quadratic algebras and skew-symmetric classical \(r\)-matrices. Zbl 1436.70005
Dubrovin, B.; Skrypnyk, T.
2
2019
Gaudin-type models, non-skew-symmetric classical \(r\)-matrices and nested Bethe ansatz. Zbl 1328.82018
Skrypnyk, T.
2
2015
Generalized Knizhnik-Zamolodchikov equations, off-shell Bethe ansatz and non-skew-symmetric classical \(r\)-matrices. Zbl 1196.81207
Skrypnyk, T.
2
2010
Spin chains in magnetic field, non-skew-symmetric classical r-matrices and BCS-type integrable systems. Zbl 1192.82025
Skrypnyk, T.
2
2009
Integrable deformations of the mKdV and SG hierarchies and quasigraded Lie algebras. Zbl 1134.37359
Skrypnyk, T.
2
2006
Integrable deformation of the Toda chain and quasigraded Lie algebras. Zbl 1109.37051
Skrypnyk, T.
2
2005
Deformations of loop algebras and classical integrable systems: finite-dimensional Hamiltonian systems. Zbl 1106.37038
Skrypnyk, T.
2
2004
Anisotropic quasigraded Lie algebras on hyperelliptic curves and integrable Hamiltonian systems. Zbl 0974.17036
Golod, P. I.; Skrypnyk, T. V.
2
2000
“Symmetric” separation of variables for the Clebsch system. Zbl 1429.70003
Skrypnyk, T.
1
2019
“Generalized” algebraic Bethe ansatz, Gaudin-type models and \(Z_{p}\)-graded classical \(r\)-matrices. Zbl 1349.82018
Skrypnyk, T.
1
2016
“Many-poled” \(r\)-matrix Lie algebras, Lax operators, and integrable systems. Zbl 1304.37050
Skrypnyk, T.
1
2014
Decompositions of quasigraded Lie algebras, non-skew-symmetric classical \(r\)-matrices and generalized Gaudin models. Zbl 1284.17017
Skrypnyk, T.
1
2014
Classical double, \(R\)-operators, and negative flows of integrable hierarchies. Zbl 1341.37035
Dubrovin, B. A.; Skrypnyk, T. V.
1
2012
Quasigraded bases in loop algebras and classical rational \(r\)-matrices. Zbl 1278.81107
Skrypnyk, T.
1
2012
Non-skew-symmetric classical r-matrices and integrable “\(p_x +ip_y\)” proton-neutron BCS models. Zbl 1262.81068
Skrypnyk, T.
1
2012
Rational r-matrices, higher rank Lie algebras and integrable proton-neutron BCS models. Zbl 1246.81075
Skrypnyk, T.
1
2012
Isomonodromic deformations, generalized Knizhnik-Zamolodchikov equations and non-skew-symmetric classical \(r\)-matrices. Zbl 1312.37045
Skrypnyk, T.
1
2010
Classical \(R\)-operators and integrable generalizations of Thirring equations. Zbl 1143.17008
Skrypnyk, Taras V.
1
2008
Quasigraded Lie algebras and modified Toda field equations. Zbl 1128.37046
Skrypnyk, Taras V.
1
2006
Quantum integrability of the generalized Euler’s top with symmetry. Zbl 0989.81041
Skrypnyk, Taras
1
2000
On the new class of commutative subalgebras of the maximal Gelfand-Kirillov dimension in the universal enveloping algebra of a simple Lie algebra. Zbl 0947.17005
Skrypnyk, T.
1
1999
Degenerate orbits of adjoint representation of orthogonal and unitary groups regarded as algebraic submanifolds. Zbl 0933.22018
Boyarskyj, O. M.; Skrypnyk, T. V.
1
1997
Separation of variables for quadratic algebras and skew-symmetric classical \(r\)-matrices. Zbl 1436.70005
Dubrovin, B.; Skrypnyk, T.
2
2019
“Symmetric” separation of variables for the Clebsch system. Zbl 1429.70003
Skrypnyk, T.
1
2019
Separation of variables for linear Lax algebras and classical \(r\)-matrices. Zbl 1403.37067
Dubrovin, B.; Skrypnyk, T.
5
2018
“Generalized” algebraic Bethe ansatz, Gaudin-type models and \(Z_{p}\)-graded classical \(r\)-matrices. Zbl 1349.82018
Skrypnyk, T.
1
2016
Quantum integrable models of interacting bosons and classical \(r\)-matrices with spectral parameters. Zbl 1326.81280
Skrypnyk, T.
4
2015
General integrable \(n\)-level, many-mode Janes-Cummings-Dicke models and classical \(r\)-matrices with spectral parameters. Zbl 1315.81114
Skrypnyk, T.
3
2015
Gaudin-type models, non-skew-symmetric classical \(r\)-matrices and nested Bethe ansatz. Zbl 1328.82018
Skrypnyk, T.
2
2015
Generalized shift elements and classical \(r\)-matrices: construction and applications. Zbl 1303.37028
Skrypnyk, T.
7
2014
“Many-poled” \(r\)-matrix Lie algebras, Lax operators, and integrable systems. Zbl 1304.37050
Skrypnyk, T.
1
2014
Decompositions of quasigraded Lie algebras, non-skew-symmetric classical \(r\)-matrices and generalized Gaudin models. Zbl 1284.17017
Skrypnyk, T.
1
2014
“\(Z_2\)-graded” Gaudin models and analytical Bethe ansatz. Zbl 1262.81064
Skrypnyk, T.
11
2013
Infinite-dimensional Lie algebras, classical \(r\)-matrices, and Lax operators: two approaches. Zbl 1328.17020
Skrypnyk, T.
6
2013
Quasi-periodic functions on the torus and \(sl(n)\)-elliptic Lie algebra. Zbl 1274.22012
Skrypnyk, T.
3
2012
Elliptic three-boson system, “two-level three-mode” JCD-type models and non-skew-symmetric classical r-matrices. Zbl 1246.82027
Skrypnyk, T.
3
2012
Classical double, \(R\)-operators, and negative flows of integrable hierarchies. Zbl 1341.37035
Dubrovin, B. A.; Skrypnyk, T. V.
1
2012
Quasigraded bases in loop algebras and classical rational \(r\)-matrices. Zbl 1278.81107
Skrypnyk, T.
1
2012
Non-skew-symmetric classical r-matrices and integrable “\(p_x +ip_y\)” proton-neutron BCS models. Zbl 1262.81068
Skrypnyk, T.
1
2012
Rational r-matrices, higher rank Lie algebras and integrable proton-neutron BCS models. Zbl 1246.81075
Skrypnyk, T.
1
2012
Lie algebras with triangular decompositions, non-skew-symmetric classical \(r\)-matrices and Gaudin-type integrable systems. Zbl 1185.81095
Skrypnyk, T.
5
2010
Integrable modifications of Dicke and Jaynes-Cummings models, Bose-Hubbard dimers and classical \(r\)-matrices. Zbl 1189.81290
Skrypnyk, T.
4
2010
Generalized Knizhnik-Zamolodchikov equations, off-shell Bethe ansatz and non-skew-symmetric classical \(r\)-matrices. Zbl 1196.81207
Skrypnyk, T.
2
2010
Isomonodromic deformations, generalized Knizhnik-Zamolodchikov equations and non-skew-symmetric classical \(r\)-matrices. Zbl 1312.37045
Skrypnyk, T.
1
2010
Integrability and superintegrability of the generalized \(n\)-level many-mode Jaynes-Cummings and Dicke models. Zbl 1283.81084
Skrypnyk, T.
7
2009
Non-skew-symmetric classical \(r\)-matrices, algebraic Bethe ansatz, and Bardeen-Cooper-Schrieffer-type integrable systems. Zbl 1202.17016
Skrypnyk, T.
5
2009
Non-skew-symmetric classical \(r\)-matrices and integrable cases of the reduced BCS model. Zbl 1181.81063
Skrypnyk, T.
4
2009
Compatible Poisson brackets, quadratic Poisson algebras and classical \(r\)-matrices. Zbl 1180.37106
Roubtsov, V.; Skrypnyk, T.
3
2009
Spin chains in magnetic field, non-skew-symmetric classical r-matrices and BCS-type integrable systems. Zbl 1192.82025
Skrypnyk, T.
2
2009
Generalized \(n\)-level Jaynes-Cummings and Dicke models, classical rational \(r\)-matrices and algebraic Bethe ansatz. Zbl 1153.81020
Skrypnyk, T.
6
2008
Dual \(R\)-matrix integrability. Zbl 1182.37037
Skrypnyk, T. V.
3
2008
Classical \(R\)-operators and integrable generalizations of Thirring equations. Zbl 1143.17008
Skrypnyk, Taras V.
1
2008
Generalized Gaudin systems in a magnetic field and non-skew-symmetric \(r\)-matrices. Zbl 1127.81023
Skrypnyk, T.
20
2007
Quantum integrable systems, non-skew-symmetric \(r\)-matrices and algebraic Bethe ansatz. Zbl 1121.81068
Skrypnyk, T.
12
2007
Generalized Gaudin spin chains, nonskew symmetric \(r\)-matrices, and reflection equation algebras. Zbl 1153.81435
Skrypnyk, Taras
10
2007
Special quasigraded Lie algebras and integrable Hamiltonian systems. Zbl 1218.37103
Skrypnyk, T.
4
2007
New non-skew symmetric classical \(r\)-matrices and ‘twisted’ quasigraded Lie algebras. Zbl 1108.37047
Skrypnyk, T.
3
2007
Integrable quantum spin chains, non-skew symmetric \(r\)-matrices and quasigraded Lie algebras. Zbl 1101.81064
Skrypnyk, T.
20
2006
Generalized quantum Gaudin spin chains, involutive automorphisms and “twisted” classical \(r\)-matrices. Zbl 1111.81087
Skrypnyk, T.
7
2006
Modified non-Abelian Toda field equations and twisted quasigraded Lie algebras. Zbl 1112.37073
Skrypnyk, T.
3
2006
Integrable deformations of the mKdV and SG hierarchies and quasigraded Lie algebras. Zbl 1134.37359
Skrypnyk, T.
2
2006
Quasigraded Lie algebras and modified Toda field equations. Zbl 1128.37046
Skrypnyk, Taras V.
1
2006
New integrable Gaudin-type systems, classical \(r\)-matrices and quasigraded Lie algebras. Zbl 1123.81369
Skrypnyk, T.
5
2005
Integrable deformation of the Toda chain and quasigraded Lie algebras. Zbl 1109.37051
Skrypnyk, T.
2
2005
Deformations of loop algebras and integrable systems: hierarchies of integrable equations. Zbl 1064.37055
Skrypnyk, T.
7
2004
‘Doubled’ generalized Landau-Lifshitz hierarchies and special quasigraded Lie algebras. Zbl 1063.22025
Skrypnyk, T.
3
2004
Deformations of loop algebras and classical integrable systems: finite-dimensional Hamiltonian systems. Zbl 1106.37038
Skrypnyk, T.
2
2004
Quasigraded deformations of loop algebras and classical integrable systems. Zbl 1047.37052
Skrypnyk, T.
10
2002
Quasigraded Lie algebras on hyperelliptic curves and classical integrable systems. Zbl 1032.17052
Skrypnyk, T.
8
2001
Hierarchies of integrable equations associated with hyperelliptic Lie algebras. Zbl 1001.37075
Skrypnyk, T.; Holod, P.
3
2001
Singular orbits of the co-adjoint representation of Euclidean groups. Zbl 0964.22018
Boyarskij, A. M.; Skrypnik, T. V.
3
2000
Anisotropic quasigraded Lie algebras on hyperelliptic curves and integrable Hamiltonian systems. Zbl 0974.17036
Golod, P. I.; Skrypnyk, T. V.
2
2000
Quantum integrability of the generalized Euler’s top with symmetry. Zbl 0989.81041
Skrypnyk, Taras
1
2000
On the new class of commutative subalgebras of the maximal Gelfand-Kirillov dimension in the universal enveloping algebra of a simple Lie algebra. Zbl 0947.17005
Skrypnyk, T.
1
1999
Degenerate orbits of adjoint representation of orthogonal and unitary groups regarded as algebraic submanifolds. Zbl 0933.22018
Boyarskyj, O. M.; Skrypnyk, T. V.
1
1997

Citations by Year