General Theory of Lie Groupoids and Lie Algebroids

This a comprehensive modern account of the theory of Lie groupoids and Lie algebroids, and their importance in differential geometry.

Kirill C. H. Mackenzie (Author)

9780521499286, Cambridge University Press

Paperback, published 9 June 2005

540 pages
22.9 x 15.2 x 3.1 cm, 0.79 kg

This a comprehensive modern account of the theory of Lie groupoids and Lie algebroids, and their importance in differential geometry, in particular their relations with Poisson geometry and general connection theory. It covers much work done since the mid 1980s including the first treatment in book form of Poisson groupoids, Lie bialgebroids and double vector bundles, as well as a revised account of the relations between locally trivial Lie groupoids, Atiyah sequences, and connections in principal bundles. As such, this book will be of great interest to all those concerned with the use of Poisson geometry as a semi-classical limit of quantum geometry, as well as to all those working in or wishing to learn the modern theory of Lie groupoids and Lie algebroids.

Part I. The General Theory: 1. Lie groupoids: fundamental theory
2. Lie groupoids: algebraic constructions
3. Lie algebroids: fundamental theory
4. Lie algebroids: algebraic constructions
Part II. The Transitive Theory: 5. Infinitesimal connection theory
6. Path connections and Lie theory
7. Cohomology and Schouten calculus
8. The cohomological obstruction
Part III. The Poisson and Symplectic Theories: 9. Double vector bundles
10. Poisson structures and Lie algebras
11. Poisson and symplectic groupoids
12. Lie bialgebroids
Appendix
Bibliography
Index.

Subject Areas: Differential & Riemannian geometry [PBMP], Algebra [PBF]