# Geometric Models for Noncommutative Algebras

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*Ana Cannas da Silva; Alan Weinstein*

A co-publication of the AMS and Center for Pure and Applied Mathematics at University of California, Berkeley

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.

This series is jointly published between the AMS and the Center for Pure and Applied Mathematics at the University of California at Berkeley (UCB CPAM).

This series is jointly published between the AMS and the Center for Pure and Applied Mathematics at the University of California at Berkeley (UCB CPAM).

#### Readership

Graduate students and research mathematicians working in symplectic and Poisson geometry and its applications to classical and quantum physics and to noncommutative algebra.

#### Reviews & Endorsements

The only available monograph on the topic, it is readable and stimulating and contains material which otherwise is only spread over the literature … The book is well done … It should be an essential purchase for mathematics libraries and is likely to be a standard reference for years to come, providing an introduction to an attractive area of further research.

-- Mathematical Reviews