Classification of $\mathcal {O}_\infty $-Stable $C^*$-Algebras (Memoirs of the American Mathematical Society)

Gabe, James

American Mathematical Society（2024/03発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 115 p.
• 言語 ENG
• 商品コード 9781470467937

Full Description

Present a proof of Kirchberg's classification theorem: two separable, nuclear, $\mathcal {O}_\infty $-Stable $C^*$-algebras are stably isomorphic if and only if they are idealrelated KK-equivalent. In particular, this provides a more elementary proof of the Kirchberg-Phillips theorem which is isolated in the paper to increase readability of this important special case.

Contents

Chapters
1. Introduction and main results
2. Equivalence of $\ast $-homomorphisms
3. Approximate domination and nuclearity
4. $\mathcal O_2$-stable and $\mathcal O_\infty $-stable $\ast $-homomorphisms
5. Absorbing representations
6. Asymptotic intertwining
7. A unitary path and some key lemmas
8. The Kirchberg-Phillips Theorem
9. Strongly $\mathcal O_\infty $-stable $\ast $-homomorphisms
10. Ideals and actions of topological spaces
11. Absorbing representations revisited
12. Ideal-related $KK$-theory
13. A stable uniqueness theorem
14. An ideal-related $\mathcal O_2$-embedding theorem
15. The main theorems