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From the Basic Homotopy Lemma to the Classification of $C^*$-algebras
・ISBN 978-1-4704-3490-8 paper US$ 55.00
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| 著者・編者 | Lin, Huaxin, |
|---|---|
| シリーズ | (CBMS Regional Conference Series in Mathematics) |
| 出版社 | (American Mathematical Society, US) |
| 出版年月 | 2017 |
| ページ数 | 240 pp. |
| 言語 | ENG |
| ニュース番号 | ＜A02-21763＞ |
解説
This book examines some recent developments in the theory of $C^*$-algebras, which are algebras of operators on Hilbert spaces. An elementary introduction to the technical part of the theory is given via a basic homotopy lemma concerning a pair of almost commuting unitaries. The book presents an outline of the background as well as some recent results of the classification of simple amenable $C^*$-algebra, otherwise known as the Elliott program. This includes some stable uniqueness theorems and a revisiting of Bott maps via stable homotopy. Furthermore, $KK$-theory related rotation maps are introduced. The book is based on lecture notes from the CBMS lecture sequence at the University of Wyoming in the summer of 2015.