Characterizing Groupoid C*-algebras of Non-Hausdorff Etale Groupoids (Paperback, 1st ed. 2022)

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.

General

Imprint:	Springer International Publishing AG
Country of origin:	Switzerland
Series:	Lecture Notes in Mathematics, 2306
Release date:	October 2022
First published:	2022
Authors:	Ruy Exel • David R. Pitts
Dimensions:	235 x 155mm (L x W)
Format:	Paperback
Pages:	158
Edition:	1st ed. 2022
ISBN-13:	978-3-03-105512-6
Categories:	Books > Science & Mathematics > Mathematics > Algebra > Groups & group theory Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis
LSN:	3-03-105512-8
Barcode:	9783031055126

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