A construction of actions on Kirchberg algebras which induce given actions on their K-groups

Details A construction of actions on Kirchberg algebras which induce given actions on their K-groups A construction of actions on Kirchberg algebras which induce given actions on their K-groups

2006-08-03

arxiv.org/abs/math/0608093v2

Mathematics

Operator Algebras

34 pages, Corrected typos

Scientific paper

We prove that every action of a finite group all of whose Sylow subgroups are cyclic on the K-theory of a Kirchberg algebra can be lifted to an action on the Kirchberg algebra. The proof uses a construction of Kirchberg algebras generalizing the one of Cuntz-Krieger algebras, and a result on modules over finite groups. As a corollary, every automorphism of the K-theory of a Kirchberg algebra can be lifted to an automorphism of the Kirchberg algebra with same order.

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