Lie Infinity-Algebras from Lie Rinehart Pairs

TL;DR

This paper extends the Schouten calculus to Lie Rinehart pairs, constructing a non-negatively graded Lie infinity-algebra on their exterior powers, advancing the algebraic framework for these structures.

Contribution

It introduces a novel generalization of Schouten calculus to Lie Rinehart pairs, establishing a Lie infinity-algebra structure on their exterior powers.

Findings

Defined a non-negatively graded Lie oo-algebra on exterior powers of Lie Rinehart pairs.

Generalized classical Schouten calculus to a broader algebraic context.

Provided a new algebraic framework for studying Lie Rinehart pairs.

Abstract

We generalize the Schouten calculus of multivector fields to commutative Lie Rinehart pairs and define a non negatively graded Lie oo-algebra on their exterior power.