General Theory of Lie Groupoids and Lie Algebroids

by Kirill C. H. Mackenzie

Overview

This comprehensive modern account of the theory of Lie groupoids and Lie algebroids reveals their importance in differential geometry, in particular, their relations with Poisson geometry and general connection theory. It covers much research since the mid 1980s, including the first analysis in book form of Poisson groupoids, Lie bialgebroids and double vector bundles. The volume will be of great interest to all learning the modern theory of Lie groupoids and Lie algebroids.

Product Details

ISBN-13:	9780521499286
Publisher:	Cambridge University Press
Publication date:	07/31/2005
Series:	London Mathematical Society Lecture Note Series , #213
Pages:	540
Product dimensions:	5.98(w) x 8.98(h) x 1.22(d)

About the Author

Kirill Mackenzie is a reader in Pure Mathematics at the University of Sheffield

Table of Contents

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.