Geometric Models for Noncommutative Algebras Ana Cannas da Silva

ISBN: 9780821809525

Published: January 1st 1999

Unknown Binding

184 pages


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Geometric Models for Noncommutative Algebras  by  Ana Cannas da Silva

Geometric Models for Noncommutative Algebras by Ana Cannas da Silva
January 1st 1999 | Unknown Binding | PDF, EPUB, FB2, DjVu, talking book, mp3, RTF | 184 pages | ISBN: 9780821809525 | 4.41 Mb

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 commutativeMoreThe 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.



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