$Classification of $/mathcal {O}_/infty $-Stable $C^*$-Algebras - James Gabe$

Classification of $/mathcal {O}_/infty $-Stable $C^*$-Algebras

James Gabe (Autor)

Buch | Softcover

115 Seiten

2024
American Mathematical Society (Verlag)
978-1-4704-6793-7 (ISBN)

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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.

James Gabe, University of Southern Denmark, Odense, Denmark.

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

Erscheinungsdatum	02.03.2024
Reihe/Serie	Memoirs of the American Mathematical Society ; Volume: 293 Number: 1461
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	272 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	1-4704-6793-3 / 1470467933
ISBN-13	978-1-4704-6793-7 / 9781470467937
Zustand	Neuware