Cohomology of Hom-Lie superalgebras and $q$-deformed Witt superalgebra

Title:

Cohomology of Hom-Lie superalgebras and $q$-deformed Witt superalgebra

Creator:

Ammar, Faouzi, Makhlouf, Abdenacer, and Saadaoul, Nejib

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:d07b2901-befa-4240-a27d-9ff6eaff65e2
uuid:d07b2901-befa-4240-a27d-9ff6eaff65e2

Subject:

Hom-Lie superalgebra, derivation, cohomology, and $q$-deformed superalgebra

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

721-761

Source:

Czechoslovak Mathematical Journal | 2013 Volume:63 | Number:3

Harvested from:

CDK

Metadata only:

false