- Hacettepe Journal of Mathematics and Statistics
- Vol: 44 Issue: 2
- On universal central extensions of Hom-Lie algebras
On universal central extensions of Hom-Lie algebras
Authors : J. M. Casas, M. A. Insua, N. Pacheco
Pages : 277-288
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Publication Date : 2015-04-01
Article Type : Research
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.Keywords : Hom-Lie algebra, homology, Hom-module, (universal) central extension, (universal) α-central extension