From the Basic Homotopy Lemma to the Classification of $C^*$-algebras (Cbms Regional Conference Series in Mathematics)

Lin, Huaxin

American Mathematical Society（2017/10発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 240 p.
• 言語 ENG
• 商品コード 9781470434908
• DDC分類 514.24

Full Description

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.

Contents

An overview of the Elliott program
An introduction to the Basic Homotopy Lemma
Maps to finite dimensional $C^*$-algebras
Stable homotopy lemmas
The Basic Homotopy Lemma, finite dimensional cases
$C^*$-algebras of generalized tracial rank one
More Basic Homotopy Lemmas
Asymptotic unitary equivalence
Classification of simple $C^*$-algebras of finite rank
Bibliography
Index