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

Abstract

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.

34 pages, Corrected typos

References in corpus (3)

• A construction of $C^{\ast }$-algebras from $C^{\ast }$-correspondences
• A Remark on Quantum Group Actions and Nuclearity
• Non-cyclotomic Presentations of Modules and Prime-order Automorphisms of Kirchberg Algebras

Cited by in corpus (1)

• Permutation presentations of modules over finite groups