Geodesic
Cohomology and deformations of 3-dimensional Heisenberg Hom-Lie superalgebras
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 2, pp. 335-350
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.21136/CMJ.2021.0310-19
Classification : 17B56, 17B60, 17B61, 17B99
Keywords: Hom-Lie superalgebra; Lie superalgebra; Heisenberg Hom-Lie superalgebra; cohomology; deformation 
@article{10_21136_CMJ_2021_0310_19,
     author = {Zhu, Junxia and Chen, Liangyun},
     title = {Cohomology and deformations of 3-dimensional {Heisenberg} {Hom-Lie} superalgebras},
     journal = {Czechoslovak Mathematical Journal},
     pages = {335--350},
     year = {2021},
     volume = {71},
     number = {2},
     doi = {10.21136/CMJ.2021.0310-19},
     mrnumber = {4263173},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0310-19/}
}
TY  - JOUR
AU  - Zhu, Junxia
AU  - Chen, Liangyun
TI  - Cohomology and deformations of 3-dimensional Heisenberg Hom-Lie superalgebras
JO  - Czechoslovak Mathematical Journal
PY  - 2021
SP  - 335
EP  - 350
VL  - 71
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0310-19/
DO  - 10.21136/CMJ.2021.0310-19
LA  - en
ID  - 10_21136_CMJ_2021_0310_19
ER  - 
%0 Journal Article
%A Zhu, Junxia
%A Chen, Liangyun
%T Cohomology and deformations of 3-dimensional Heisenberg Hom-Lie superalgebras
%J Czechoslovak Mathematical Journal
%D 2021
%P 335-350
%V 71
%N 2
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0310-19/
%R 10.21136/CMJ.2021.0310-19
%G en
%F 10_21136_CMJ_2021_0310_19
Zhu, Junxia; Chen, Liangyun. Cohomology and deformations of 3-dimensional Heisenberg Hom-Lie superalgebras. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 2, pp. 335-350. doi: 10.21136/CMJ.2021.0310-19

[1] Alvarez, M. A., Cartes, F.: Cohomology and deformations for the Heisenberg Hom-Lie algebras. Linear Multilinear Algebra 67 (2019), 2209-2229. | DOI | MR | JFM

[2] Ammar, F., Ejbehi, Z., Makhlouf, A.: Cohomology and deformations of Hom-algebras. J. Lie Theory 21 (2011), 813-836. | MR | JFM

[3] Ammar, F., Makhlouf, A.: Hom-Lie superalgebras and Hom-Lie admissible superalgebras. J. Algebra 324 (2010), 1513-1528. | DOI | MR | JFM

[4] Ammar, F., Makhlouf, A., Saadaoui, N.: Cohomology of Hom-Lie superalgebras and $q$-deformed Witt superalgebra. Czech. Math. J. 63 (2013), 721-761. | DOI | MR | JFM

[5] Liu, Y., Chen, L., Ma, Y.: Hom-Nijienhuis operators and $T^*$-exentions of Hom-Lie superalgebras. Linear Algebra Appl. 439 (2013), 2131-2144. | DOI | MR | JFM

[6] Makhlouf, A., Silvestrov, S.: Notes on 1-parameter formal deformations of Hom-associative and Hom-Lie algebras. Forum Math. 22 (2010), 715-739. | DOI | MR | JFM

[7] Peniche, R., Sánchez-Valenzuela, O. A.: On Heisenberg-like super group structures. Ann. Henri Poincaré 10 (2010), 1395-1417. | DOI | MR | JFM

[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. | DOI | MR | JFM

[9] Sheng, Y.: Representations of Hom-Lie algebras. Algebr. Represent. Theory 15 (2012), 1081-1098. | DOI | MR | JFM

[10] Wang, C., Zhang, Q., Wei, Z.: A classification of low dimensional multiplicative Hom-Lie superalgebras. Open Math. 14 (2016), 613-628. | DOI | MR | JFM

[11] Wang, Z.: A Classification of Low Dimensional Lie Superalgebras: Master Thesis. East China Normal University, Shanghai (2006), Chinese.

Cité par Sources :