On universal central extensions of Hom-Lie algebras

By José Manuel Casas, Manuel A. Insua, N. P. Rego. 2012

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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 $\alpha$-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 $\alpha$-central extensions. A homological characterization of universal ($\alpha$)-central extensions is given.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fbee2fb01b0dd66bf73473454fa8ea66b6edbce5