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arXiv · 1209.5887

On universal central extensions of Hom-Lie algebras

J. M. Casas·M. A. Insua·N. Pacheco
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Abstract

We develop a theory of universal central extensions of Hom-Lie algebras. Classical results of universal central extensions of Lie algebras cannot be completely extended to Hom-Lie algebras setting, because of the composition of two central extensions is not central. This fact leads to introduce the notion of universal $α$-central extension. Classical results as the existence of a universal central extension of a perfect Hom-Lie algebra remains true, but others as the central extensions of the middle term of a universal central extension is split only holds for $α$-central extensions. A homological characterization of universal ($α$)-central extensions is given.

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BibTeXRIS

J. M. Casas, M. A. Insua, N. Pacheco. 2012-09-26. On universal central extensions of Hom-Lie algebras. https://arxiv.org/abs/1209.5887

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