Split extensions of BiHom-Lie algebras

TL;DR

This paper introduces the concept of split extensions in BiHom-Lie algebras, develops their cohomology, and establishes a classification correspondence with second cohomology groups.

Contribution

It defines split extensions for BiHom-Lie algebras, constructs their cohomology, and links extension classes to second cohomology, advancing the structural understanding of these algebras.

Findings

Defined split extensions of BiHom-Lie algebras.

Constructed the cohomology theory for these extensions.

Established a bijective correspondence with second cohomology groups.

Abstract

In this paper, we introduce the notion of split extension of BiHom- Lie algebra and construct the corresponding cohomology. Also, we establish a one-to-one correspondence between the equivalence classes of extensions of a BiHom-Lie algebra L by an abelian BiHom-Lie algebra V and its second cohomology group.