Characterizing Groupoid C*-algebras of Non-Hausdorff Étale Groupoids
PAYBACK Punkte
17 °P sammeln!
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...
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 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.
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 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.
Andere Kunden interessierten sich für
