Cohomology of morphism Lie algebras and some applications

Abstract

A morphism Lie algebra is a triple $(\mathfrak{g},\mathfrak{h},\varphi )$ consisting of two Lie algebras $\mathfrak{g},\mathfrak{h}$ and a Lie algebra homomorphism $\varphi :\mathfrak{g}\to \mathfrak{h}$. We define representations and cohomology of morphism Lie algebras. As applications of our cohomology, we study some aspects of deformations, abelian extensions of morphism Lie algebras and classify skeletal morphism sh Lie algebras. Finally, we consider the cohomology of morphism Lie groups and find a relation with the cohomology of morphism Lie algebras.

17 pages; Submitted for publication

References in corpus (1)

• Cohomology of weighted Rota-Baxter Lie algebras and Rota-Baxter paired operators