Deformations and Extensions of BiHom-alternative algebras

Year 2023, Volume: 34 Issue: 34, 159 - 181, 10.07.2023

Taoufik Chtıouı Sami Mabrouk Abdenacer Makhlouf

https://doi.org/10.24330/ieja.1260492

Abstract

The aim of this paper is to deal with BiHom-alternative algebras which are a generalization of alternative and
Hom-alternative algebras, their structure is defined with two
commuting multiplicative linear maps. We study cohomology and
one-parameter formal deformation theory of left BiHom-alternative
algebras. Moreover, we study central and $T_\theta$-extensions of
BiHom-alternative algebras and their relationship with
cohomology.
Finally, we investigate generalized derivations and give some relevant results.

Keywords

BiHom-alternative algebra, representation, cohomology, formal deformation, extension

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