On universal central extensions of Hom-Lie algebras

Year 2015, Volume: 44 Issue: 2, 277 - 288, 01.04.2015

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

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

References

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