num_pages: 184
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.
language: English
title: Geometric Models for Noncommutative Algebras
publisher: American Mathematical Society(RI)