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

Yanhui BiDanlu ChenTao Zhang
Feb 2022
摘要
In this paper, we introduce the concept of crossed module forHom-Leibniz-Rinehart algebras. We study the cohomology and extension theory ofHom-Leibniz-Rinehart algebras. It is proved that there is one-to-onecorrespondence between equivalence classes of abelian extensions ofHom-Leibniz-Rinehart algebras and the elements of second cohomology group.Furthermore, we prove that there is a natural map from $\alpha$-crossed modulesextension of Hom-Leibniz-Rinehart algebras to the third cohomology group ofHom-Leibniz-Rinehart algebras.
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