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


Journal of Generalized Lie Theory and Applications

Author(s): Faouzi Ammar, Abdenacer Makhlouf, Nejib Saadaoui

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Hom-Lie algebra (superalgebra) structure appeared naturally in q-deformations, based on σ-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 αk-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 osp(1, 2) superalgebra and q-deformed Witt superalgebra.

This article was published in Czechoslovak Mathematical Journal and referenced in Journal of Generalized Lie Theory and Applications

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