| eBook ISBN: | 978-1-4704-4377-1 |
| Product Code: | MEMO/252/1204.E |
| List Price: | $78.00 |
| MAA Member Price: | $70.20 |
| AMS Member Price: | $46.80 |
| eBook ISBN: | 978-1-4704-4377-1 |
| Product Code: | MEMO/252/1204.E |
| List Price: | $78.00 |
| MAA Member Price: | $70.20 |
| AMS Member Price: | $46.80 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 252; 2018; 141 ppMSC: Primary 46; Secondary 20
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.
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Table of Contents
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Chapters
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Introduction
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1. Preliminaries
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2. Orbit space groupoids and Fell bundles
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3. $^*$-Algebraic crossed product by a Hecke pair
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4. Direct limits of sectional algebras
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5. Reduced $C^*$-crossed products
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6. Other completions
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7. Stone-Von Neumann Theorem For Hecke Pairs
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8. Towards Katayama duality
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Additional Material
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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.
-
Chapters
-
Introduction
-
1. Preliminaries
-
2. Orbit space groupoids and Fell bundles
-
3. $^*$-Algebraic crossed product by a Hecke pair
-
4. Direct limits of sectional algebras
-
5. Reduced $C^*$-crossed products
-
6. Other completions
-
7. Stone-Von Neumann Theorem For Hecke Pairs
-
8. Towards Katayama duality
