bokomslag Characterizing Groupoid C*-algebras of Non-Hausdorff tale Groupoids
Vetenskap & teknik

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

Ruy Exel David R Pitts

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  • 158 sidor
  • 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 KumjianRenault 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 KumjianRenault theory toa 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.
  • Författare: Ruy Exel, David R Pitts
  • Format: Pocket/Paperback
  • ISBN: 9783031055126
  • Språk: Engelska
  • Antal sidor: 158
  • Utgivningsdatum: 2022-10-20
  • Förlag: Springer International Publishing AG