2021/10/05 by Apurba Das, Das, Apurba
Mathematics · #17B55 #17B56 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2110.01971
openalex publication_date 2021/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A morphism Lie algebra is a triple (\mathfrakg, \mathfrakh, ϕ) consisting of two Lie algebras \mathfrakg, \mathfrakh and a Lie algebra homomorphism ϕ: \mathfrakg → \mathfrakh. 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.