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Lecture Notes in Mathematics Ser.: Characterizing Groupoid C*-Algebras of Non-Hausdorff Etale Groupoids by Ruy Exel and David R. Pitts (2022, Trade Paperback)
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- Buy it nowCharacterizing Groupoid C*-Algebras of Non-Hausdorff �tale Groupoids (Paperback
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About this product
Product Identifiers
PublisherSpringer International Publishing A&G
ISBN-103031055128
ISBN-139783031055126
eBay Product ID (ePID)20057278033
Product Key Features
Number of PagesVIII, 158 Pages
Publication NameCharacterizing Groupoid C*-Algebras of Non-Hausdorff Etale Groupoids
LanguageEnglish
Publication Year2022
SubjectAlgebra / Abstract, Functional Analysis
TypeTextbook
AuthorRuy Exel, David R. Pitts
Subject AreaMathematics
SeriesLecture Notes in Mathematics Ser.
FormatTrade Paperback
Dimensions
Item Weight9.4 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Reviews"The book under review generalizes Kumjian and Renault's work to include more examples of C*-algebras. In doing this, the noncommutative space used is allowed to be non-Hausdorff. Non-Hausdorff groupoids have been the source of many exciting examples or counterexamples. As such, a better study of non-Hausdorff groupoids is welcome. ... The book ends with a section of examples and open questions. The Appendix contains details of a fundamental result in the theory of twisted groupoid C_-algebras." (Cristian Ivanescu, Mathematical Reviews, November, 2023) "This is a nicely written monograph devoted to the new and important notion of non Hausdorff groupoids and their C*-algebras, and could be beneficial for researchers in operator algebras and mathematical physics." (Massoud Amini, zbMATH 1511.46002, 2023), "This is a nicely written monograph devoted to the new and important notion of non Hausdorff groupoids and their C*-algebras, and could be beneficial for researchers in operator algebras and mathematical physics." (Massoud Amini, zbMATH 1511.46002, 2023)
Series Volume Number2306
Number of Volumes1 vol.
IllustratedYes
Table Of Content- 1. Introduction. - 2. Inclusions. - 3. Groupoids. - 4. Examples and Open Questions. - 5. Appendix.
SynopsisThis book develops tools to handle C*-algebras arising as completions of convolution algebras of sections of line bundles over possibly non-Hausdorff groupoids. A fundamental result of Gelfand describes commutative C*-algebras as continuous functions on locally compact Hausdorff spaces. Kumjian, and later Renault, showed that Gelfand's result can be extended to include non-commutative C*-algebras containing a commutative C*-algebra. In their setting, the C*-algebras in question may be described as the completion of convolution algebras of functions on twisted Hausdorff groupoids with respect to a certain norm. However, there are many natural settings in which the Kumjian-Renault theory does not apply, in part because the groupoids which arise are not Hausdorff. In fact, non-Hausdorff groupoids have been a source of surprising counterexamples and technical difficulties for decades. Including numerous illustrative examples, this book extends the Kumjian-Renault theory toa much broader class of C*-algebras. This work will be of interest to researchers and graduate students in the area of groupoid C*-algebras, the interface between dynamical systems and C*-algebras, and related fields.
LC Classification NumberQA319-329.9
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