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Equivariant one-parameter deformations of associative algebras. (English) Zbl 1440.13064

Summary: We introduce an equivariant version of Hochschild cohomology as the deformation cohomology to study equivariant deformations of associative algebras equipped with finite group actions.

MSC:

13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)
13D10 Deformations and infinitesimal methods in commutative ring theory
14D15 Formal methods and deformations in algebraic geometry
16E40 (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.)
55M35 Finite groups of transformations in algebraic topology (including Smith theory)
55N91 Equivariant homology and cohomology in algebraic topology
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References:

[1] Fialowski, A. and Fuchs, D., Construction of miniversal deformation of Lie algebras, J. Funct. Anal.161 (1999) 76-110. · Zbl 0944.17015
[2] Fialowski, A., Mandal, A. and Mukherjee, G., Versal deformations of Leibniz algebras, J. K-Theory3(2) (2009) 327-358. · Zbl 1191.17001
[3] Fox, T. F., An introduction to algebraic deformation theory, J. Pure Appl. Algebra84(1) (1993) 17-41. · Zbl 0772.18006
[4] Gerstenhaber, M., The Cohomology structure of an associative ring, Ann. Math.78 (1963) 267-288. · Zbl 0131.27302
[5] Gerstenhaber, M., On the Deformation of rings and algebras, Ann. Math.79 (1964) 59-103. · Zbl 0123.03101
[6] Gerstenhaber, M., On the Deformation of rings and algebras, Ann. Math.84 (1966) 1-19. · Zbl 0147.28903
[7] Gerstenhaber, M., On the Deformation of rings and algebras, Ann. Math.88 (1968) 1-34. · Zbl 0182.05902
[8] Gerstenhaber, M., On the Deformation of rings and algebras, Ann. Math.99 (1974) 257-276. · Zbl 0281.16016
[9] Gerstenhaber, M. and Schack, S. D., On the deformation of algebra morphisms and diagrams, Trans. Amer. Math. Soc.279(1) (1983) 1-50. · Zbl 0544.18005
[10] Gerstenhaber, M. and Schack, S. D., On the cohomology of an algebra morphism, J. Algebra95 (1985) 245-262. · Zbl 0595.16021
[11] Loday, J.-L., Cyclic Homology, , Vol. 301 (Springer, 1992). · Zbl 0780.18009
[12] Loday, J.-L., Une version non commutative des algèbres de Lie: les algèbres de Leibniz, Ens. Math.39(3-4) (1993) 269-293. · Zbl 0806.55009
[13] Loday, J.-L., Overview on Leibniz algebras, dialgebras and their homology, Fields Inst. Commun.17 (1997) 91-102. · Zbl 0893.17001
[14] Loday, J.-L., Dialgebras and Related Operads, , Vol. 1763 (Springer, Berlin, 2001), pp. 7-66. · Zbl 0970.00010
[15] Majumdar, A. and Mukherjee, G., Deformation theory of dialgebras, K-Theory27 (2002) 33-60. · Zbl 1016.16026
[16] Majumdar, A. and Mukherjee, G., Errata: Deformation theory of dialgebras, K-Theory35(3-4) (2005) 395-397. · Zbl 1101.16306
[17] Mandal, A., Deformation of Leibniz algebra morphisms, Homol. Homot. Appl.9(1) (2007) 439-450. · Zbl 1162.17002
[18] Mandal, A. and Mukherjee, G., Deformation of Leibniz algebra morphisms over commutative local algebra base, Comm. Algebra37(7) (2009) 2246-2266. · Zbl 1171.13010
[19] Nijenhuis, A. and Richardson, R. W., Cohomology and deformations in graded Lie algebras, Bull. Amer. Math. Soc.72 (1966) 1-29. · Zbl 0136.30502
[20] Nijenhuis, A. and Richardson, R. W., Deformations of homomorphisms of Lie algebras, Bull. Amer. Math. Soc.73 (1967) 175-179. · Zbl 0153.04402
[21] Nijenhuis, A. and Richardson, R. W. Jr., Deformations of Lie algebra structures, J. Math. Mech.17 (1967) 89-105. · Zbl 0166.30202
[22] Yau, D., Deformation of dual Leibniz algebra morphisms, Comm. Algebra35(4) (2007) 1369-1378. · Zbl 1232.17005
[23] Yau, D., Deformation theory of dialgebra morphisms, Algebra Colloq.15(2) (2008) 279-292. · Zbl 1177.17004
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