Overview

In the 1990s, it has become increasingly clear that there are important mathematical connections relating the three mathematical concepts - groupoids, inverse semigroups, and operator algebras. There has been much progress in this area and this text presents an account of the subject. The book should appeal to professional mathematicians and graduate students in fields such as operator algebars, analysis of groupoids, semi-group theory, and noncommutative geometry. It should also be of interest to mathematicians interested in tilings and to theoretical physicists whose focus is modelling quasicrystals with tilings.

Full Product Details

Author:   Alan Paterson
Publisher:   Birkhauser Boston Inc
Imprint:   Birkhauser Boston Inc
Edition:   1999 ed.
Volume:   170
Dimensions:   Width: 15.50cm , Height: 1.70cm , Length: 23.50cm
Weight:   1.310kg
ISBN:  

9780817640514

ISBN 10:   0817640517
Pages:   274
Publication Date:   01 October 1998
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Awaiting stock  
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Table of Contents

1. Introduction.- 2. Inverse Semigroups and Locally Compact Groupoids.- 2.1 Inverse semigroups.- 2.2 Locally compact and r-discrete groupoids.- 2.3 Lie groupoids.- 3. Groupoid C*-Algebras and Their Relation to Inverse Semigroup Covariance C*-Algebras.- 3.1 Representation theory for locally compact groupoids.- 3.2 Representation theory for groupoids that are r-discrete, and their inverse semigroups of open G-sets.- 3.3 Groupoid and covariance C*-algebras.- 4. The Groupoid C*-Algebras of Inverse Semigroups.- 4.1 Introduction.- 4.2 Examples of inverse semigroups and their associated groupoids.- 4.3 The universal groupoid of an inverse semigroup.- 4.4 Inverse semigroup universal and reduced C*-algebras as groupoid C*-algebras.- 4.5 Amenability of the von Neumann algebra of an inverse semigroup.- Appendix A. Amenability for Inverse Semigroups.- Appendix B. Groupoid Amenability and Locally Compact Groups.- Appendix C. The Measurability of Fg.- Appendix D. Ind ? as an Induced Representation.- Appendix E. Guichardet’s Disintegration Theorem.- Appendix F. Some Differential Topology.- Index of Terms.- Index of Symbols.

Reviews

This outstanding book brings together three mathematical objects 'which a priori seem to have nothing much in common'.a ]The concept of amenability is largely carried over to the present framework. In particular, Clifford semigroups are examined. An example coming from physics, quasicrystals, is discussed. Throughout the monograph explicit clear proofs are provided. The large coverage of this material makes pleasant reading. <p>a Zentralblatt Math

This outstanding book brings together three mathematical objects 'which a priori seem to have nothing much in common'.!The concept of amenability is largely carried over to the present framework. In particular, Clifford semigroups are examined. An example coming from physics, quasicrystals, is discussed. Throughout the monograph explicit clear proofs are provided. The large coverage of this material makes pleasant reading. --Zentralblatt Math

This outstanding book brings together three mathematical objects 'which a priori seem to have nothing much in common'...The concept of amenability is largely carried over to the present framework. In particular, Clifford semigroups are examined. An example coming from physics, quasicrystals, is discussed. Throughout the monograph explicit clear proofs are provided. The large coverage of this material makes pleasant reading. -Zentralblatt Math

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