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＜電子ブック＞
Characterizing Groupoid C*-algebras of Non-Hausdorff Étale Groupoids / by Ruy Exel, David R. Pitts
(Lecture Notes in Mathematics. ISSN:16179692 ; 2306)

版	1st ed. 2022.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2022
大きさ	VIII, 158 p : online resource
著者標目	*Exel, Ruy author Pitts, David R author SpringerLink (Online service)
件　名	LCSH:Functional analysis LCSH:Group theory FREE:Functional Analysis FREE:Group Theory and Generalizations
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-031-05513-3

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