Abelian extensions and crossed modules of Hom-Lie algebras
J. M. Casas
Abstract
In this paper we study the low dimensional cohomology groups of Hom-Lie algebras and their relation with derivations, abelian extensions and crossed modules. On one hand, we introduce the notion of α-abelian extensions and we obtain a five term exact sequence in cohomology. On the other hand, we study crossed modules of Hom-Lie algebras showing their equivalence with cat1-Hom-Lie algebras, and we introduce α-crossed modules to have a better understanding of the third cohomology grou
Topics & Concepts
MathematicsCohomologyPure mathematicsEquivalence (formal languages)Abelian groupLie algebraAlgebra over a fieldAdvanced Topics in AlgebraAlgebraic structures and combinatorial modelsSphingolipid Metabolism and Signaling