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arXiv · 2402.10845

Cyclic Lie-Rinehart algebras

Daniel Beltita·Alina Dobrogowska·Grzegorz Jakimowicz
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Abstract

We study Lie-Rinehart algebra structures in the framework provided by a duality pairing of modules over a unital commutative associative algebra. Thus, we construct examples of Lie brackets corresponding to a fixed anchor map whose image is a cyclic submodule of the derivation module, and therefore we call them cyclic Lie-Rinehart algebras. In a very special case of our construction, these brackets turn out to be related to certain differential operators that occur in mathematical physics.

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Daniel Beltita, Alina Dobrogowska, Grzegorz Jakimowicz. 2024-02-16. Cyclic Lie-Rinehart algebras. https://arxiv.org/abs/2402.10845

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