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SIGMA 4 (2008), 005, 30 pages arXiv:0710.3098
https://doi.org/10.3842/SIGMA.2008.005
Contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson
Poisson Manifolds, Lie Algebroids, Modular Classes: a Survey
Yvette Kosmann-Schwarzbach
Centre de Mathématiques Laurent Schwartz,
École Polytechnique, 91128 Palaiseau, France
Received August 31, 2007, in final form January
02, 2008; Published online January 16, 2008
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.
Key words:
Poisson geometry; Poisson cohomology; modular classes; twisted Poisson structures; Lie algebroids; Gerstenhaber algebras; Lie algebroid cohomology; triangular r-matrices; quasi-Frobenius algebras; pure spinors.
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