Kirchberg Algebras Research Articles

Non-cyclotomic presentations of modules and prime-order automorphisms of Kirchberg algebras

We prove the following theorem: let $A$ be a UCT Kirchberg algebra, and let $\alpha$ be a prime-order automorphism of $K_*(A)$, with $\alpha([1_A])=[1_A]$ in case $A$ is unital. Then $\alpha$ is induced from an automorphism of $A$ having the same order as $\alpha$. This result is extended to certain instances of an equivariant inclusion of Kirchberg algebras. As a crucial ingredient we prove the following result in representation theory: every module over the integral group ring of a cyclic group of prime order has a natural presentation by generalized lattices with no cyclotomic summands.

Continuous fields of Kirchberg [formula omitted]-algebras

In this paper we study the C * -algebras associated to continuous fields over locally compact metrizable zero-dimensional spaces whose fibers are Kirchberg C * -algebras satisfying the UCT. We show that these algebras are inductive limits of finite direct sums of Kirchberg algebras and they are classified up to isomorphism by topological invariants.