Poisson Geometry, Deformation Quantisation and Group Representations
[Book]
edited by Simone Gutt, John Rawnsley, Daniel Sternheimer.
Cambridge
Cambridge University Press
2005
(370 p.).
London Mathematical Society Lecture Note Series, no. 323.
Pt. 1. Poisson geometry and Morita equivalence --; 1. Introduction --; 2. Poisson geometry and some generalizations --; 3. Algebraic Morita equivalence --; 4. Geometric Morita equivalence --; 5. Geometric representation equivalence --; pt. 2. Formality and star products --; 1. Introduction --; 2. The star product --; 3. Rephrasing the main problem : the formality --; 4. Digression : what happens in the dual --; 5. The Kontsevich formula --; 6. From local to global deformation quantization --; pt. 3. Lie groupoids, sheaves and cohomology --; 1. Introduction --; 2. Lie groupoids --; 3. Sheaves on Lie groupoids --; 4. Sheaf cohomology --; 5. Compactly supported cohomology --; pt. 4. Geometric methods in representation theory.
An accessible introduction to Poisson geometry suitable for graduate students.
edited by Simone Gutt, John Rawnsley, Daniel Sternheimer.