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Geometric Models for Noncommutative Algebras
     

Geometric Models for Noncommutative Algebras

by Ana Cannas de Silva, Alan Weinstein
 

ISBN-10: 0821809520

ISBN-13: 9780821809525

Pub. Date: 03/09/1999

Publisher: American Mathematical Society

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

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.

Product Details

ISBN-13:
9780821809525
Publisher:
American Mathematical Society
Publication date:
03/09/1999
Series:
Berkley Mathematics Lecture Notes Series , #10
Pages:
184
Product dimensions:
7.09(w) x 9.84(h) x (d)

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