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 Paper

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 insert ignore into journalissuearticles values(α);- central extensions is given. 
Keywords : Hom Lie algebra, homology, Hom module universal, central extension universal, α central extension