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

Häftad, Engelska, 2024

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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.

Produktinformation

Utgivningsdatum2024-03-31
Mått178 x 254 x undefined mm
Vikt272 g
FormatHäftad
SpråkEngelska
SerieMemoirs of the American Mathematical Society
Antal sidor115
FörlagAmerican Mathematical Society
ISBN9781470467937

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Beräkning och matematisk analys inom Naturvetenskap och teknik

Chapters1. Introduction and main results2. Equivalence of $\ast $-homomorphisms3. Approximate domination and nuclearity4. $\mathcal O_2$-stable and $\mathcal O_\infty $-stable $\ast $-homomorphisms5. Absorbing representations6. Asymptotic intertwining7. A unitary path and some key lemmas8. The Kirchberg-Phillips Theorem9. Strongly $\mathcal O_\infty $-stable $\ast $-homomorphisms10. Ideals and actions of topological spaces11. Absorbing representations revisited12. Ideal-related $KK$-theory13. A stable uniqueness theorem14. An ideal-related $\mathcal O_2$-embedding theorem15. The main theorems