TY  - GEN
AB  - 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 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.
AU  - Exel, Ruy,
AU  - Pitts, David Ryder,
CN  - QA326
DO  - 10.1007/978-3-031-05513-3
DO  - doi
ID  - 1450509
KW  - C*-algebras.
KW  - Groupoids.
LK  - https://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-05513-3
N2  - 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 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.
SN  - 9783031055133
SN  - 3031055136
T1  - Characterizing groupoid C* -algebras of non-Hausdorff Étale groupoids /
TI  - Characterizing groupoid C* -algebras of non-Hausdorff Étale groupoids /
UR  - https://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-05513-3
VL  - volume 2306
ER  -