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Table of contents (4 chapters)
Keywords
About this book
In recent years, it has become increasingly clear that there are important connections relating three concepts -- groupoids, inverse semigroups, and operator algebras. There has been a great deal of progress in this area over the last two decades, and this book gives a careful, up-to-date and reasonably extensive account of the subject matter.
After an introductory first chapter, the second chapter presents a self-contained account of inverse semigroups, locally compact and r-discrete groupoids, and Lie groupoids. The section on Lie groupoids in chapter 2 contains a detailed discussion of groupoids particularly important in noncommutative geometry, including the holonomy groupoids of a foliated manifold and the tangent groupoid of a manifold. The representation theories of locally compact and r-discrete groupoids are developed in the third chapter, and it is shown that the C*-algebras of r-discrete groupoids are the covariance C*-algebras for inverse semigroup actions on locally compact Hausdorff spaces. A final chapter associates a universal r-discrete groupoid with any inverse semigroup. Six subsequent appendices treat topics related to those covered in the text.
The book should appeal to a wide variety of professional mathematicians and graduate students in fields such as operator algebras, analysis on groupoids, semigroup theory, and noncommutative geometry. It will also be of interest to mathematicians interested in tilings and theoretical physicists whose focus is modeling quasicrystals with tilings. An effort has been made to make the book lucid and 'user friendly"; thus it should be accessible to any reader with a basic background in measure theory and functional analysis.
Reviews
"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
Authors and Affiliations
Bibliographic Information
Book Title: Groupoids, Inverse Semigroups, and their Operator Algebras
Authors: Alan L. T. Paterson
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/978-1-4612-1774-9
Publisher: Birkhäuser Boston, MA
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media New York 1999
Hardcover ISBN: 978-0-8176-4051-4Published: 01 October 1998
Softcover ISBN: 978-1-4612-7276-2Published: 08 October 2012
eBook ISBN: 978-1-4612-1774-9Published: 06 December 2012
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 1
Number of Pages: XVI, 274
Topics: Group Theory and Generalizations, Operator Theory, Topological Groups, Lie Groups