RT Journal Article T1 Abelian extensions and crossed modules of Hom-Lie algebras A1 Casas Mirás, José Manuel A1 García Martínez, Xabier K1 12 Matemáticas K1 1201.09 Álgebra de Lie AB 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 PB Journal of Pure and Applied Algebra SN 00224049 YR 2020 FD 2020-03 LK http://hdl.handle.net/11093/7907 UL http://hdl.handle.net/11093/7907 LA eng NO Journal of Pure and Applied Algebra, 224(3): 987-1008 (2020) NO Agencia Estatal de Investigación | Ref. MTM2016-79661-P DS Investigo RD 17-feb-2025