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

ABSTRACT

We construct homology with trivial coefficients of Hom-Leibniz n-algebras. We introduce and characterize universal ()-central extensions of Hom-Leibniz n-algebras. In particular, we show their interplay with the zero-th and first homology with trivial coefficients. When 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 universal central extensions. A generalization of the concept and properties of unicentral Leibniz algebras to the setting of Hom-Leibniz n-algebras is developed.

KEYWORDS:

• Hom-Leibniz n-algebra
• universal ()-central extension
• perfect Hom-Leibniz n-algebra
• non-abelian tensor product
• unicentral Hom-Leibniz n-algebra

AMS SUBJECT CLASSIFICATIONS:

• 17A30
• 17B55
• 18G60

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

First author was supported by Ministerio de Economía y Competitividad (Spain), [grant number MTM2016-79661-P] (AEI/FEDER, UE, support included).