Geometric Models For Noncommutative Algebras

Download

E-Book Overview

The volume is based on a course, "Geometric Models for Noncommutative Algebras" taught by Professor Weinstein at Berkeley. 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. An extensive bibliography and index are included.

E-Book Content

Geometric Models for Noncommutative Algebras Ana Cannas da Silva1 Alan Weinstein2 University of California at Berkeley December 1, 1998 1 2 [email protected], [email protected] [email protected] Contents Preface xi Introduction I Universal Enveloping Algebras
You might also like

Computational Chemistry: A Practical Guide For Applying Techniques To Real World Problems
Authors: David Young    235    0

Heuristic And Optimization For Knowledge Discovery
Authors: Ruhul Sarker , Hussein A. Abbass , Charles Newton    268    0

Computationalism: New Directions
Authors: Matthias Scheutz    264    0

Computer Algebra Recipes For Mathematical Physics
Authors: Richard H. Enns    168    0

Digital Signal And Image Processing Using Matlab
Authors: Gérard Blanchet , Maurice Charbit    177    0

Python Scripting For Computational Science
Authors: Hans Petter Langtangen    196    0

Mathematical Writing
Authors: Donald E. Knuth    221    0

Galois Theory, U Glasgow Course
Authors: John B. Fraleigh    249    0

Frobenius Splitting Methods In Geometry And Representation Theory
Authors: Michel Brion , Shrawan Kumar (auth.)    232    0

Set Theory
Authors: Thomas Jech    270    0