Format:
1 Online-Ressource(VIII, 158 p.)
Edition:
1st ed. 2022.
ISBN:
9783031055133
Series Statement:
Lecture Notes in Mathematics 2306
Content:
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.
Additional Edition:
ISBN 9783031055126
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9783031055126
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9783031055140
Additional Edition:
Erscheint auch als Druck-Ausgabe Exel, Ruy, 1956 - Characterizing groupoid C*-algebras of non-Hausdorff étale groupoids Cham, Switzerland : Springer Nature, 2022 ISBN 9783031055126
Language:
English
Keywords:
Gruppoid
;
C-Stern-Subalgebra
;
Linienbündel
DOI:
10.1007/978-3-031-05513-3
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