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arXiv · 1901.03087

On Hom-Lie antialgebra

Tao Zhang·Heyu Zhang
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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.

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Tao Zhang, Heyu Zhang. 2019-01-10. On Hom-Lie antialgebra. https://doi.org/10.1080/00927872.2020.1731519

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