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Cohomology and deformations of 3-dimensional Heisenberg Hom-Lie superalgebras. (English) Zbl 07361072

Summary: We study Hom-Lie superalgebras of Heisenberg type. For 3-dimensional Heisenberg Hom-Lie superalgebras we describe their Hom-Lie super structures, compute the cohomology spaces and characterize their infinitesimal deformations.

MSC:

17B56 Cohomology of Lie (super)algebras
17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)
17B61 Hom-Lie and related algebras
17B99 Lie algebras and Lie superalgebras
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[1] Alvarez, M. A.; Cartes, F., Cohomology and deformations for the Heisenberg Hom-Lie algebras, Linear Multilinear Algebra 67 (2019), 2209-2229 · Zbl 1477.17076
[2] Ammar, F.; Ejbehi, Z.; Makhlouf, A., Cohomology and deformations of Hom-algebras, J. Lie Theory 21 (2011), 813-836 · Zbl 1237.17003
[3] Ammar, F.; Makhlouf, A., Hom-Lie superalgebras and Hom-Lie admissible superalgebras, J. Algebra 324 (2010), 1513-1528 · Zbl 1258.17008
[4] Ammar, F.; Makhlouf, A.; Saadaoui, N., Cohomology of Hom-Lie superalgebras and \(q\)-deformed Witt superalgebra, Czech. Math. J. 63 (2013), 721-761 · Zbl 1299.17018
[5] Liu, Y.; Chen, L.; Ma, Y., Hom-Nijienhuis operators and \(T^*\)-exentions of Hom-Lie superalgebras, Linear Algebra Appl. 439 (2013), 2131-2144 · Zbl 1281.17033
[6] Makhlouf, A.; Silvestrov, S., Notes on 1-parameter formal deformations of Hom-associative and Hom-Lie algebras, Forum Math. 22 (2010), 715-739 · Zbl 1201.17012
[7] Peniche, R.; Sánchez-Valenzuela, O. A., On Heisenberg-like super group structures, Ann. Henri Poincaré 10 (2010), 1395-1417 · Zbl 1206.81066
[8] Rodríguez-Vallarte, M.; Salgado, G.; Sánchez-Valenzuela, O. A., Heisenberg Lie superalgebras and their invariant superorthogonal and supersymplectic forms, J. Algebra 332 (2011), 71-86 · Zbl 1264.17007
[9] Sheng, Y., Representations of Hom-Lie algebras, Algebr. Represent. Theory 15 (2012), 1081-1098 · Zbl 1294.17001
[10] Wang, C.; Zhang, Q.; Wei, Z., A classification of low dimensional multiplicative Hom-Lie superalgebras, Open Math. 14 (2016), 613-628 · Zbl 1345.17020
[11] Wang, Z., A Classification of Low Dimensional Lie Superalgebras: Master Thesis, East China Normal University, Shanghai (2006), Chinese
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