This article is cited in 35 papers

Poisson Manifolds, Lie Algebroids, Modular Classes: a Survey

Yvette Kosmann-Schwarzbach

Centre de Mathématiques Laurent Schwartz, Ècole Polytechnique, 91128 Palaiseau, France

Abstract: After a brief summary of the main properties of Poisson manifolds and Lie algebroids in general, we survey recent work on the modular classes of Poisson and twisted Poisson manifolds, of Lie algebroids with a Poisson or twisted Poisson structure, and of Poisson–Nijenhuis manifolds. A review of the spinor approach to the modular class concludes the paper.

Keywords: Poisson geometry; Poisson cohomology; modular classes; twisted Poisson structures; Lie algebroids; Gerstenhaber algebras; Lie algebroid cohomology; triangular $r$-matrices; quasi-Frobenius algebras; pure spinors.

MSC: 17B70; 17B56; 17B66; 53C15; 58A10; 15A66; 17B81; 17-02; 53-02; 58-02

Received: August 31, 2007; in final form January 2, 2008; Published online January 16, 2008

Language: English

DOI: 10.3842/SIGMA.2008.005

Bibliographic databases:

• 
• 
• 
• 

ArXiv: 0710.3098