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

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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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Authors and Affiliations

  1. University of Sfax, Sfax, Tunisia

    Faouzi Ammar & Nejib Saadaoui

  2. University of Haute Alsace, Mulhouse, France

    Abdenacer Makhlouf

Authors
  1. Faouzi Ammar
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  2. Abdenacer Makhlouf
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  3. Nejib Saadaoui
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Correspondence to Faouzi Ammar.

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Ammar, F., Makhlouf, A. & Saadaoui, N. Cohomology of Hom-Lie superalgebras and q-deformed Witt superalgebra. Czech Math J 63, 721–761 (2013). https://doi.org/10.1007/s10587-013-0049-6

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  • DOI: https://doi.org/10.1007/s10587-013-0049-6

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