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

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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.

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Acknowledgements

We would like to thank the referee for careful reading and for valuable suggestions on this paper. This research was supported by the National Natural Science Foundation of China (No. 11961049) and by the Key Project of Jiangxi Natural Science Foundation grant (No. 20232ACB201004).

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Authors and Affiliations

  1. College of Mathematics and Information Science, Nanchang Hangkong University, Nanchang, 330063, China

    Yanhui Bi & Danlu Chen

  2. College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, China

    Tao Zhang

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  1. Yanhui Bi
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  2. Danlu Chen
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  3. Tao Zhang
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Correspondence to Tao Zhang.

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Bi, Y., Chen, D. & Zhang, T. Cohomology and Crossed Module Extensions of Hom-Leibniz–Rinehart Algebras. Front. Math (2024). https://doi.org/10.1007/s11464-022-0351-4

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