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9781470451332 Academic Inspection Copy

A Tool Kit for Groupoid $C^{*}$-Algebras

  • ISBN-13: 9781470451332
  • Publisher: AMERICAN MATHEMATICAL SOCIETY
    Imprint: AMERICAN MATHEMATICAL SOCIETY
  • By Dana P. Williams
  • Price: AUD $338.00
  • Stock: 0 in stock
  • Availability: This book is temporarily out of stock, order will be despatched as soon as fresh stock is received.
  • Local release date: 30/10/2019
  • Format: Hardback (254.00mm X 178.00mm) 404 pages Weight: 925g
  • Categories: Algebra [PBF]
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The construction of a $C^{*}$-algebra from a locally compact groupoid is an important generalization of the group $C^{*}$-algebra construction and of the transformation group $C^{*}$-algebra construction. Since their introduction in 1980, groupoid $C^{*}$-algebras have been intensively studied with diverse applications, including graph algebras, classification theory, variations on the Baum-Connes conjecture, and noncommutative geometry. This book provides a detailed introduction to this vast subject and is suitable for graduate students or any researcher who wants to use groupoid $C^{*}$-algebras in their work. The main focus is to equip the reader with modern versions of the basic technical tools used in the subject, which will allow the reader to understand fundamental results and make contributions to various areas in the subject. Thus, in addition to covering the basic properties and construction of groupoid $C^{*}$-algebras, the focus is to give a modern treatment of some of the major developments in the subject in recent years, including the Equivalence Theorem and the Disintegration Theorem. Also covered are the complicated subjects of amenability of groupoids and simplicity results. The book is reasonably self-contained and accessible to graduate students with a good background in operator algebras.
Dana P. Williams, Dartmouth College, Hanover, NH.
From groupoid to algebra Groupoid actions and equivalence Measure theory Proof of the Equivalence Theorem Basic representation theory The existence and uniqueness of Haar systems Unitary representations Renault's Disintegration Theorem Amenability for groupoids Measurewise amenability for groupoids Comments on simplicity Duals and topological vector spaces Remarks on Blanchard's Theorem The inductive limit topology Ramsay almost everywhere Answers to some of the exercises Notation and symbol index Index Bibliography.
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