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9781470467937 Academic Inspection Copy

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

  • ISBN-13: 9781470467937
  • Publisher: AMERICAN MATHEMATICAL SOCIETY
    Imprint: AMERICAN MATHEMATICAL SOCIETY
  • By James Gabe
  • Price: AUD $219.00
  • Stock: 0 in stock
  • Availability: This book is temporarily out of stock, order will be despatched as soon as fresh stock is received.
  • Local release date: 29/06/2024
  • Format: Paperback (254.00mm X 178.00mm) 115 pages Weight: 272g
  • Categories: Calculus & mathematical analysis [PBK]
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Biography
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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
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