Journal ArticleDOI
A new proof of Kirchberg's 2-stable classification
TLDR
In this article, a new proof of Kirchberg's stable classification theorem was presented, which states that two separable, nuclear, stable/unital, α-algebras are isomorphic if and only if their ideal lattices are order isomorphic, or equivalently, their primitive ideal spaces are homeomorphic.Abstract:
I present a new proof of Kirchberg’s
O
2
-stable classification theorem: two separable, nuclear, stable/unital,
O
2
-stable
C
∗
-algebras are isomorphic if and only if their ideal lattices are order isomorphic, or equivalently, their primitive ideal spaces are homeomorphic. Many intermediate results do not depend on pure infiniteness of any sort.read more
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The classification of Rokhlin flows on C*-algebras
TL;DR: In this paper, the authors studied flows on C *-algebras with the Rokhlin property up to cocycle conjugacy, and showed that every Kirchberg algebra carries a unique RokHlin flow up to the point when the cone of lower-semicontinuous traces is affinely conjugate.
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On a categorical framework for classifying C*-dynamics up to cocycle conjugacy
TL;DR: In this paper, a categorical approach to the classification of C*-dynamics up to cocycle conjugacy is presented. But the main aim of this paper is to generalize the fundamental intertwining results commonly employed in the Elliott program for classifying C* -algebras.
Journal ArticleDOI
The classification of Rokhlin flows on C*-algebras
TL;DR: In this paper, it was shown that every Kirchberg algebra carries a unique Rokhlin flow up to cocycle conjugacy, which confirms a long-standing conjecture of Kishimoto.
Journal ArticleDOI
Traceless AF embeddings and unsuspended E -theory
TL;DR: In this article, it was shown that quasidiagonality and AF embeddability are equivalent properties for traceless lattice-algebras and are characterised in terms of the primitive ideal space.
The dynamical Kirchberg-Phillips theorem
James Gabe,G'abor Szab'o +1 more
TL;DR: In this article , the authors studied amenable G -actions on Kirchberg algebras that admit an approximately central embedding of a canonical quasi-free action on the Cuntz algebra O ∞ .
References
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Book
C*-Algebras and Finite-Dimensional Approximations
TL;DR: In this article, the authors present a classification of group von Neumann algebras based on the following properties: weak expectation property, local lifting property, and local reflexivity.
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