The Characteristic Class of a Lie Algebra Ideal, Contact Structures and the Poisson Algebra of Basic Functions

TL;DR

This paper explores the algebraic properties of Lie algebra ideals, contact structures, and Poisson algebras, focusing on cohomology classes, Poisson cohomology, and geometric quantization.

Contribution

It introduces a new algebraic framework linking Lie algebra ideals, contact geometry, and Poisson structures, advancing understanding of their cohomological aspects.

Findings

Identification of specific cohomology classes related to Lie algebra ideals

Analysis of Poisson cohomology in contact structures

Insights into geometric (pre)quantization processes

Abstract

Some cohomology classes associated with an ideal in a Lie algebra, a Poisson structure on the basic functions algebra of contact structure, its Poisson cohomology and geometric (pre)quantization are considered from the algebraic point of view.