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Characterizing groupoid C*-algebras of non-Hausdorff Étale groupoids

Record Type:	Electronic resources : Monograph/item
Title/Author:	Characterizing groupoid C*-algebras of non-Hausdorff Étale groupoidsby Ruy Exel, David R. Pitts.
Author:	Exel, Ruy.
other author:	Pitts, David Ryder.
Published:	Cham :Springer International Publishing :2022.
Description:	viii, 158 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	C*-algebras.
Online resource:	https://doi.org/10.1007/978-3-031-05513-3
ISBN:	9783031055133$q(electronic bk.)

Characterizing groupoid C*-algebras of non-Hausdorff Étale groupoids
Exel, Ruy.

Characterizing groupoid C*-algebras of non-Hausdorff Étale groupoids[electronic resource] /by Ruy Exel, David R. Pitts. - Cham :Springer International Publishing :2022. - viii, 158 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 23061617-9692 ;. - Lecture notes in mathematics ;2035..

This 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 to a 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.

ISBN: 9783031055133$q(electronic bk.)

Standard No.: 10.1007/978-3-031-05513-3doiSubjects--Topical Terms:

306364
C*-algebras.

LC Class. No.: QA326 / .E84 2022

Dewey Class. No.: 512.55

Characterizing groupoid C*-algebras of non-Hausdorff Étale groupoids
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490 1 $a Lecture notes in mathematics, $x 1617-9692 ; $v v. 2306
520 $a This 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 to a 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.
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650 1 4 $a Functional Analysis. $3 274845
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