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arXiv · 1802.04061

Abelian extensions and crossed modules of Hom-Lie algebras

José-Manuel Casas·Xabier García-Martínez
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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 $\alpha$-abelian extensions and we obtain a five term exact sequence in cohomology. On the other hand, we introduce crossed modules of Hom-Lie algebras showing their equivalence with cat$^1$-Hom-Lie algebras, and we introduce $\alpha$-crossed modules to have a better understanding of the third cohomology group.

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José-Manuel Casas, Xabier García-Martínez. 2018-02-12. Abelian extensions and crossed modules of Hom-Lie algebras. https://arxiv.org/abs/1802.04061

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