| Title:
|
Cohomology of Hom-Lie superalgebras and $q$-deformed Witt superalgebra (English) |
| Author:
|
Ammar, Faouzi |
| Author:
|
Makhlouf, Abdenacer |
| Author:
|
Saadaoui, Nejib |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
63 |
| Issue:
|
3 |
| Year:
|
2013 |
| Pages:
|
721-761 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Hom-Lie algebra (superalgebra) structure appeared naturally in $q$-deformations, based on $\sigma $-derivations of Witt and Virasoro algebras (superalgebras). They are a twisted version of Lie algebras (superalgebras), obtained by deforming the Jacobi identity by a homomorphism. In this paper, we discuss the concept of $\alpha ^k$-derivation, a representation theory, and provide a cohomology complex of Hom-Lie superalgebras. Moreover, we study central extensions. As application, we compute derivations and the second cohomology group of a twisted ${\rm osp}(1,2)$ superalgebra and $q$-deformed Witt superalgebra. (English) |
| Keyword:
|
Hom-Lie superalgebra |
| Keyword:
|
derivation |
| Keyword:
|
cohomology |
| Keyword:
|
$q$-deformed superalgebra |
| MSC:
|
17A70 |
| MSC:
|
17B56 |
| MSC:
|
17B68 |
| idZBL:
|
Zbl 06282107 |
| idMR:
|
MR3125651 |
| DOI:
|
10.1007/s10587-013-0049-6 |
| . |
| Date available:
|
2013-10-07T12:06:09Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143486 |
| . |
| Reference:
|
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