A non-abelian Hom-Leibniz tensor product and applications

Abstract

The notion of non-abelian Hom–Leibniz tensor product is introduced and some properties are established. This tensor product is used in the description of the universal (-)central extensions of Hom–Leibniz algebras. We also give its application to the Hochschild homology of Hom-associative algebras.

Keywords:

• Hom–Leibniz algebra
• non-abelian tensor product
• universal ()-central extension
• Hom-associative algebra
• Hochschild homology

AMS Subject Classifications:

• 17A30
• 17B55
• 17B60
• 18G35
• 18G60

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first and the second authors were supported by Ministerio de Economía y Competitividad (Spain) (European FEDER support included), [grant number MTM2016-79661-P]. The second author was also supported by Shota Rustaveli National Science Foundation, [grant number FR/189/5-113/14].