Deformations and Extensions of BiHom-alternative algebras

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.