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On Hom-Lie Pseudo-Superalgebras

DOI: 10.4236/apm.2016.66029, PP. 420-435

Keywords: Hom-Associative Pseudo-Superalgebra, Hom-Lie Pseudo-Superalgebra, Hom-Lie Conformal Superalgebra, Hom-Annihilation Superalgebra, Cohomology

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Abstract:

The aim of this article is to introduce the notion of Hom-Lie H-pseudo-superalgebras for any Hopf algebra H. This class of algebras is a natural generalization of the Hom-Lie pseudo-algebras as well as a special case of the Hom-Lie superalgebras. We present some construction theorems of Hom-Lie H-pseudo-superalgebras, reformulate the equivalent definition of Hom-Lie H-pseudo-super-algebras, and consider the cohomology theory of Hom-Lie H-pseudo-superalgebras with coefficients in arbitrary Hom-modules as a generalization of Kac’s result.

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