Abelian extensions and crossed modules of Hom-Lie algebras
DATA:
2020-03
IDENTIFICADOR UNIVERSAL: http://hdl.handle.net/11093/7907
VERSIÓN EDITADA: https://linkinghub.elsevier.com/retrieve/pii/S0022404919301641
TIPO DE DOCUMENTO: article
RESUMO
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
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