Cohomology of Hom-Lie superalgebras and q-deformed Witt superalgebra |
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Authors: | Faouzi Ammar Abdenacer Makhlouf Nejib Saadaoui |
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Affiliation: | 1. University of Sfax, Sfax, Tunisia 2. University of Haute Alsace, Mulhouse, France
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Abstract: | 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 α 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 osp(1, 2) superalgebra and q-deformed Witt superalgebra. |
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