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arXiv · 2103.15006

Extensions and crossed modules of $n$-Lie Rinehart algebras

A. Ben Hassine·T. Chtioui·M. Elhamdadi·S. Mabrouk
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Abstract

We introduce a notion of $n$-Lie Rinehart algebras as a generalization of Lie Rinehart algebras to $n$-ary case. This notion is also an algebraic analogue of $n$-Lie algebroids. We develop representation theory and describe a cohomology complex of $n$-Lie Rinehart algebras. Furthermore, we investigate extension theory of $n$-Lie Rinehart algebras by means of $2$-cocycles. Finally, we introduce crossed modules of $n$-Lie Rinehart algebras to gain a better understanding of their third dimensional cohomology groups.

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BibTeXRIS

A. Ben Hassine, T. Chtioui, M. Elhamdadi, S. Mabrouk. 2021-03-27. Extensions and crossed modules of $n$-Lie Rinehart algebras. https://arxiv.org/abs/2103.15006

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