Alina Dobrogowska
Cyclic Lie–Rinehart algebras
We study Lie--Rinehart algebra structures in a framework provided by duality pairings of modules over unital commutative associative algebra. Thus, we construct new examples of Lie bracke ts 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. Special cases of our construction include Lie algebroid structures on cotangent bundles of differential manifolds and also certain differential operators that occur in mathematical physics.
