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arXiv · 2202.09224

Cohomology and crossed modules extension of Hom-Leibniz-Rinehart algebras

Yanhui Bi·Danlu Chen·Tao Zhang
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Abstract

In this paper, we introduce the concept of crossed module for Hom-Leibniz-Rinehart algebras. We study the cohomology and extension theory of Hom-Leibniz-Rinehart algebras. It is proved that there is 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 $\alpha$-crossed modules extension of Hom-Leibniz-Rinehart algebras to the third cohomology group of Hom-Leibniz-Rinehart algebras.

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Yanhui Bi, Danlu Chen, Tao Zhang. 2022-02-13. Cohomology and crossed modules extension of Hom-Leibniz-Rinehart algebras. https://arxiv.org/abs/2202.09224

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