EAN: 9783031055126

Bilder-Quelle: discount24.de - Sport-Freizeit

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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