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Crossed Products by Hecke Pairs.
・ISBN 978-1-4704-2809-9 paper US$ 78.00
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| 著者・編者 | Palma, Rui, |
|---|---|
| シリーズ | Memoirs of the American Mathematical Society |
| 出版社 | (American Mathematical Society, US) |
| 出版年月 | 2018 |
| ページ数 | 141 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-13244＞ |
解説
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 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.