On Lie Algebroids and Poisson Algebras

TL;DR

This paper introduces a new class of Lie algebroids related to Poisson algebras, providing classification results and new insights into their structure and connections.

Contribution

It defines and studies Lie algebroids associated with faithful modules, inspired by cotangent Lie algebroids of Poisson manifolds, and classifies transitive Lie algebroids.

Findings

Classified transitive Lie algebroids.

Connected Poisson algebras with Lie algebroid structures.

Described Poisson algebras using algebroid and Lie connections.

Abstract

We introduce and study a class of Lie algebroids associated to faithful modules which is motivated by the notion of cotangent Lie algebroids of Poisson manifolds. We also give a classification of transitive Lie algebroids and describe Poisson algebras by using the notions of algebroid and Lie connections.