The volume is based on a course, "Geometric Models for Noncommutative Algebras" taught by Professor Weinstein. Noncommutative geometry is the study of noncommutative algebras as if they were algebras of functions on spaces, for example, the commutative algebras associated to affine algebraic varieties, differentiable manifolds, topological spaces, and measure spaces. In this work, the authors discuss several types of geometric objects (in the usual sense of sets with structure) that are closely related to noncommutative algebras. Central to the discussion are symplectic and Poisson manifolds, which arise when noncommutative algebras are obtained by deforming commutative algebras. The authors also give a detailed study of groupoids (whose role in noncommutative geometry has been stressed by Connes) as well as of Lie algebroids, the infinitesimal approximations to differentiable groupoids. Featured are many interesting examples, applications, and exercises. The book starts with basic definitions and builds to (still) open questions. It is suitable for use as a graduate text and an extensive bibliography and index are included.
- ISBN10 0821809520
- ISBN13 9780821809525
- Publish Date 15 March 1999
- Publish Status Transferred
- Publish Country US
- Imprint American Mathematical Society
- Format Paperback
- Pages 184
- Language English