Universal α-central extensions of hom-Leibniz n-algebras

2016/07/04 by Casas, J. M., Rego, N. Pacheco
#17A30 #17B55 #18G60 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1607.00767

Abstract

We construct homology with trivial coefficients of Hom-Leibniz n-algebras. We introduce and characterize universal (α)-central extensions of Hom-Leibniz n-algebras. In particular, we show their interplay with the zeroth and first homology with trivial coefficients. When n=2 we recover the corresponding results on universal central extensions of Hom-Leibniz algebras. The notion of non-abelian tensor product of Hom-Leibniz n-algebras is introduced and we establish its relationship with the universal central extensions. We develop a generalization of the concept and properties of unicentral Leibniz algebras to the setting of Hom-Leibniz n-algebras.

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