On Hom-Lie antialgebra
Rings and Algebras
2021-02-24 v4
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.
Cite
@article{arxiv.1901.03087,
title = {On Hom-Lie antialgebra},
author = {Tao Zhang and Heyu Zhang},
journal= {arXiv preprint arXiv:1901.03087},
year = {2021}
}
Comments
19pages, no figures, some English, misprint, errors are corrected