Universal Central Extensions and Non-abelian tensor product of Hom-Lie-Rinehart Algebras

TL;DR

This paper explores the structure of universal central extensions and non-abelian tensor products in hom-Lie-Rinehart algebras, extending concepts of automorphisms and derivations to these algebraic frameworks.

Contribution

It introduces the theory of universal $ ext{ extalpha}$-central extensions and the lifting of automorphisms and $ ext{ extalpha}$-derivations in hom-Lie-Rinehart algebras, expanding existing algebraic concepts.

Findings

Development of universal $ ext{ extalpha}$-central extensions

Lifting of automorphisms to central extensions

Lifting of $ ext{ extalpha}^k$-derivations to central extensions

Abstract

In this paper we study universal central extensions and non-abelian tensor product of hom-Lie-Rinehart algebras. We discuss about universal $\alpha$- central extensions, and, lifting of automorphisms and $\alpha$-derivations to central extensions for hom-Lie-Rinehart algebras. This is in turn provide such lifting of automorphisms and $\alpha^k$-derivations to the central extensions for hom-Lie algebras.