Representations of Bihom-Lie algebras

TL;DR

This paper explores the cohomology and representation theory of Bihom-Lie algebras, a generalization of Hom-Lie algebras with two commuting maps, including derivations, extensions, and key representations.

Contribution

It provides a detailed study of derivations, extensions, and fundamental representations of Bihom-Lie algebras, advancing understanding of their structure and properties.

Findings

Analysis of derivations and central extensions

Characterization of trivial and adjoint representations

Development of cohomology theory for Bihom-Lie algebras

Abstract

Bihom-Lie algebra is a generalized Hom-Lie algebra endowed with two commuting multiplicative linear maps. In this paper, we study cohomology and representations of Bihom-Lie algebras. In particular, derivations, central extensions, derivation extensions, the trivial representation and the adjoint representation of Bihom-Lie algebras are studied in detail.