Cyclic Lie-Rinehart algebras
Differential Geometry
2024-02-19 v1 Mathematical Physics
math.MP
Rings and Algebras
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.
Cite
@article{arxiv.2402.10845,
title = {Cyclic Lie-Rinehart algebras},
author = {Daniel Beltita and Alina Dobrogowska and Grzegorz Jakimowicz},
journal= {arXiv preprint arXiv:2402.10845},
year = {2024}
}
Comments
17 pages