A new proof of the Kirchberg-Phillips theorem
نویسنده
چکیده
Cartan subalgebras, automorphisms and the UCT problem Selçuk Barlak This talk deals with the connection between the UCT problem for separable, nuclear C*-algebras and Cartan subalgebras, that is, MASAs that admit faithful conditional expectations and whose normalizers generate the ambient C*-algebras. We present a characterization, in terms of Cartan subalgebras, of the UCT for fixed point algebras of outer actions by finite cyclic groups on unital UCT Kirchberg algebras that are approximately representable in the sense of Izumi and absorb the trivial action on a suitable UHF algebra tensorially. In particular, such a fixed point algebra satisfies the UCT if and only if the action preserves some Cartan subalgebra. Combining this with earlier results obtained with G. Szabó, we provide a characterization of the UCT problem in terms of Cartan subalgebras and finite order automorphisms of the Cuntz algebra. This is joint work with Xin Li. Villadsen algebras and some regularity conditions Joan Bosa Villadsen algebras, introduced by Villadsen in a couple of articles back in the 90s, fall into two types of unital, simple and separable AH algebras, exhibiting a wide range of exotic behaviour; arbitrary stable and real rank, arbitrary radius of comparison, and perforation in their ordered K0 groups and Cuntz semigroups. In this talk, I will explain the basics about these algebras, and how we have shown that the Villadsen algebra of infinite type, V∞, does not satisfy the Corona Factorization Property neither ω-comparison. This is a joint work with M. Christensen. Elements of KK-theory and the UCT Marius Dadarlat I plan for a friendly introduction to KK-theory, the Universal Coefficient Theorem for the Kasparov groups and its cousin, the Universal Multi-Coefficient Theorem. If time allows, we shall discuss some applications of these theorems to classification theory of nuclear C*-algebras. An introduction to the Universal Coefficient Theorem Søren Eilers I will attempt to provide an introduction to the UCT of Rosenberg and Schochet, its importance in particular in classification, its various generalizations, and the open questions concerning the class of C*-algebras to which it applies.
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