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  3. Funktionsanalyse og transformation

Characterizing Groupoid C*-algebras of Non-Hausdorff Etale Groupoids

Af: Ruy Exel, David R. Pitts Engelsk Paperback

Characterizing Groupoid C*-algebras of Non-Hausdorff Etale Groupoids

Af: Ruy Exel, David R. Pitts Engelsk Paperback
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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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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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Se mere i:
Produktdetaljer
Sprog: Engelsk
Sider: 158
ISBN-13: 9783031055126
Indbinding: Paperback
Udgave:
ISBN-10: 3031055128
Kategori: Funktionsanalyse og transformation
Udg. Dato: 20 okt 2022
Længde: 0mm
Bredde: 155mm
Højde: 235mm
Forlag: Springer International Publishing AG
Oplagsdato: 20 okt 2022
Forfatter(e): Ruy Exel, David R. Pitts
Forfatter(e) Ruy Exel, David R. Pitts

Kategori Funktionsanalyse og transformation

ISBN-13 9783031055126

Sprog Engelsk

Indbinding Paperback

Sider 158

Udgave

Længde 0mm

Bredde 155mm

Højde 235mm

Udg. Dato 20 okt 2022

Oplagsdato 20 okt 2022

Forlag Springer International Publishing AG

Kategori sammenhænge