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

2002/05/19 by Zakaria Giunashvili, Giunashvili, Zakaria
Mathematics · Physics and Astronomy · #53D17 #53D35 #58B34 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG) #math-ph #math.MP #math.SG #msc:53D17 #msc:53D35 #msc:58B34

paper · pdf · doi:10.48550/arxiv.math-ph/0205025

31 pages. Some misprints and inaccuracies in definitions are corrected

openalex publication_date 2002/05/19 · arxiv created 2002/05/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Poisson cohomology of "book" Poisson structures
• Poisson cohomology and quantization
• Poisson structures on associated with rigid Lie algebras
• Central Simple Poisson Algebras
• Poisson Structures on Trivial Extension Algebras