Geometric models for noncommutative algebras
Author(s)
Bibliographic Information
Geometric models for noncommutative algebras
（Berkeley mathematics lecture notes, v. 10）
American Mathematical Society , Berkeley Center for Pure and Applied Mathematics, c1999
Available at 33 libraries
Note
Includes bibliographical references (p. 163-173) and index
Description and Table of Contents
Description
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.
Table of Contents
- UNIVERSAL ENVELOPING ALGEBRAS
- Algebraic constructions
- The Poincare-Birkhoff-Witt theorem
- POISSON GEOMETRY
- Poisson structures
- Normal forms
- Local Poisson geometry
- POISSON CATEGORY
- Poisson maps
- Hamiltonian actions
- DUAL PAIRS
- Operator algebras
- Dual pairs in Poisson geometry
- Examples of symplectic realizations
- GENERALIZED FUNCTIONS
- Group algebras
- Densities
- GROUPOIDS
- Groupoids
- Groupoid algebras
- Extended groupoid algebras
- ALGEBROIDS
- Lie algebroids
- Examples of Lie algebroids
- Differential geometry for Lie algebroids
- DEFORMATIONS OF ALGEBRAS OF FUNCTIONS
- Algebraic deformation theory
- Weyl algebras
- Deformation quantization.
by "Nielsen BookData"