On Hom-Lie antialgebra

Abstract

In this paper, we introduced the notion of Hom-Lie antialgebras. The representations and cohomology theory of Hom-Lie antialgebras are investigated. We prove that the equivalent classes of abelian extensions of Hom-Lie antialgebras are in one-to-one correspondence to elements of the second cohomology group. We also prove that 1-parameter infinitesimal deformation of a Hom-Lie antialgebra are characterized by 2-cocycles of this Hom-Lie antialgebra with adjoint representation in itself. The notion of Nijenhuis operators of Hom-Lie antialgebra is introduced to describe trivial deformations.

19pages, no figures, some English, misprint, errors are corrected

References in corpus (6)

• Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras
• BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras
• Non-commutative Hom-Poisson algebras
• Representations and cohomologies of Hom-Lie-Yamaguti algebras with applications
• On universal central extensions of Hom-Lie algebras
• Crossed modules for Hom-Lie antialgebras

Cited by in corpus (1)

• Universal central extensions of Hom-Lie antialgebras