NONNUCLEAR SUBALGEBRAS OF AF ALGEBRAS By MARIUS DADARLAT

Some Remarks on the Universal Coefficient Theorem in Kk-theory

If a nuclear separable C*-algebra A can be approximated by C*-subalgebras satisfying the UCT, then A satisfies the UCT. It is also shown that the validity of the UCT for all separable nuclear C*-algebras is equivalent to a certain finite dimensional approximation property.

Morphisms of Simple Tracially Af Algebras

Let A, B be separable simple unital tracially AF C*-algebras. Assuming that A is exact and satisfies the Universal Coefficient Theorem (UCT) in KK-theory, we prove the existence, and uniqueness modulo approximately inner automorphisms, of nuclear ∗-homomorphisms from A to B with prescribed K-theory data. This implies the AF-embeddability of separable exact residually finite dimensional C*-algeb...

One-parameter Continuous Fields of Kirchberg Algebras. Ii

Parallel to the first two authors’ earlier classification of separable unital oneparameter continuous fields of Kirchberg algebras with torsion free K-groups supported in one dimension, one-parameter separable unital continuous fields of AF-algebras are classified by their ordered K0-sheaves. We prove Effros-Handelman-Shen type theorems for separable unital one-parameter continuous fields of AF...

Residually Finite Dimensional C*-algebras and Subquotients of the Car Algebra

It is proved that the cone of a separable nuclearly embeddable residually finite-dimensional C*-algebra embeds in the CAR algebra (the UHF algebra of type 2∞). As a corollary we obtain a short new proof of Kirchberg’s theorem asserting that a separable unital C*-algebra A is nuclearly embeddable if and only there is a semisplit extension 0 → J → E → A → 0 with E a unital C*-subalgebra of the CA...

On the classification of nuclear C-algebras