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Noncommutative Spaces and Algebras of Functions

Chapter
Part of the Lecture Notes in Physics book series (LNPMGR, volume 51)

Abstract

The starting idea of noncommutative geometry is the shift from spaces to algebras of functions defined on them. In general, one has only the algebra and there is no analogue of space whatsoever. In this Chapter we shall give some general facts about algebras of (continuous) functions on (topological) spaces. In particular we shall try to make some sense of the notion of a ‘noncommutative space’.

Keywords

Topological Space Irreducible Representation Compact Operator Maximal Ideal Structure Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

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