English

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.

Keywords

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

R2 v1 2026-06-23T07:07:53.291Z