Article
| Title: | Cohomology and deformations of 3-dimensional Heisenberg Hom-Lie superalgebras (English) |
| Author: | Zhu, Junxia |
| Author: | Chen, Liangyun |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 71 |
| Issue: | 2 |
| Year: | 2021 |
| Pages: | 335-350 |
| Summary lang: | English |
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| Category: | math |
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| 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. (English) |
| Keyword: | Hom-Lie superalgebra |
| Keyword: | Lie superalgebra |
| Keyword: | Heisenberg Hom-Lie superalgebra |
| Keyword: | cohomology |
| Keyword: | deformation |
| MSC: | 17B56 |
| MSC: | 17B60 |
| MSC: | 17B61 |
| MSC: | 17B99 |
| idZBL: | 07361072 |
| idMR: | MR4263173 |
| DOI: | 10.21136/CMJ.2021.0310-19 |
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| Date available: | 2021-05-20T13:40:00Z |
| Last updated: | 2021-10-21 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/148908 |
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| Reference: | [1] Alvarez, M. A., Cartes, F.: Cohomology and deformations for the Heisenberg Hom-Lie algebras.Linear Multilinear Algebra 67 (2019), 2209-2229. Zbl 07116666, MR 4002345, 10.1080/03081087.2018.1487379 |
| Reference: | [2] Ammar, F., Ejbehi, Z., Makhlouf, A.: Cohomology and deformations of Hom-algebras.J. Lie Theory 21 (2011), 813-836. Zbl 1237.17003, MR 2917693 |
| Reference: | [3] Ammar, F., Makhlouf, A.: Hom-Lie superalgebras and Hom-Lie admissible superalgebras.J. Algebra 324 (2010), 1513-1528. Zbl 1258.17008, MR 2673748, 10.1016/j.jalgebra.2010.06.014 |
| Reference: | [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, MR 3125651, 10.1007/s10587-013-0049-6 |
| Reference: | [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, MR 3090460, 10.1016/j.laa.2013.06.006 |
| Reference: | [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, MR 2661446, 10.1515/forum.2010.040 |
| Reference: | [7] Peniche, R., Sánchez-Valenzuela, O. A.: On Heisenberg-like super group structures.Ann. Henri Poincaré 10 (2010), 1395-1417. Zbl 1206.81066, MR 2593111, 10.1007/s00023-010-0020-0 |
| Reference: | [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, MR 2774679, 10.1016/j.jalgebra.2011.02.003 |
| Reference: | [9] Sheng, Y.: Representations of Hom-Lie algebras.Algebr. Represent. Theory 15 (2012), 1081-1098. Zbl 1294.17001, MR 2994017, 10.1007/s10468-011-9280-8 |
| Reference: | [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, MR 3552510, 10.1515/math-2016-0056 |
| Reference: | [11] Wang, Z.: A Classification of Low Dimensional Lie Superalgebras: Master Thesis.East China Normal University, Shanghai (2006), Chinese. |
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