Cohomology and Crossed Module Extensions of Hom-Leibniz–Rinehart Algebras

Abstract

In this paper, we introduce the concept of crossed module for Hom-Leibniz–Rinehart algebras. We then study the cohomology and extension theory of Hom-Leibniz–Rinehart algebras. It is proved that there is a one-to-one correspondence between equivalence classes of abelian extensions of Hom-Leibniz–Rinehart algebras and the elements of second cohomology group. Furthermore, we prove that there is a natural map from α-crossed module extensions of Hom-Leibniz–Rinehart algebras to the third cohomology group of Hom-Leibniz–Rinehart algebras.

Keywords

Hom-Leibniz–Rinehart algebras / crossed modules / cohomology

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