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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.

Universal central extensions and non-abelian tensor product of hom-Lie–Rinehart algebras