Crossed Products by Hecke Pairs
Seiten
2018
American Mathematical Society (Verlag)
978-1-4704-2809-9 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-2809-9 (ISBN)
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Develops a theory of crossed products by actions of Hecke pairs $(G, /Gamma )$, motivated by applications in non-abelian $C^*$-duality. The author’s approach gives back the usual crossed product construction whenever $G / /Gamma $ is a group and retains many of the aspects of crossed products by groups.
The author develops a theory of crossed products by actions of Hecke pairs $(G, /Gamma )$, motivated by applications in non-abelian $C^*$-duality. His approach gives back the usual crossed product construction whenever $G / /Gamma $ is a group and retains many of the aspects of crossed products by groups.
The author starts by laying the $^*$-algebraic foundations of these crossed products by Hecke pairs and exploring their representation theory and then proceeds to study their different $C^*$-completions. He establishes that his construction coincides with that of Laca, Larsen and Neshveyev whenever they are both definable and, as an application of his theory, he proves a Stone-von Neumann theorem for Hecke pairs which encompasses the work of an Huef, Kaliszewski and Raeburn.
The author develops a theory of crossed products by actions of Hecke pairs $(G, /Gamma )$, motivated by applications in non-abelian $C^*$-duality. His approach gives back the usual crossed product construction whenever $G / /Gamma $ is a group and retains many of the aspects of crossed products by groups.
The author starts by laying the $^*$-algebraic foundations of these crossed products by Hecke pairs and exploring their representation theory and then proceeds to study their different $C^*$-completions. He establishes that his construction coincides with that of Laca, Larsen and Neshveyev whenever they are both definable and, as an application of his theory, he proves a Stone-von Neumann theorem for Hecke pairs which encompasses the work of an Huef, Kaliszewski and Raeburn.
Rui Palma, University of Oslo, Norway.
Introduction
Preliminaries
Orbit space groupoids and Fell bundles
$^*$-Algebraic crossed product by a Hecke pair
Direct limits of sectional algebras
Reduced $C^*$-crossed products
Other completions
Stone-von Neumann Theorem for Hecke pairs
Towards Katayama duality
Bibliography
Symbol index
Word index
| Erscheinungsdatum | 07.01.2018 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 235 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-4704-2809-1 / 1470428091 |
| ISBN-13 | 978-1-4704-2809-9 / 9781470428099 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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