TY - JOUR

T1 - A construction of actions on Kirchberg algebras which induce given actions on their K-groups

AU - Katsura, Takeshi

N1 - Funding Information:
Acknowledgments. The author is grateful to the referee for careful reading. This work was partially supported by JSPS Research Fellow.
Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2008/4

Y1 - 2008/4

N2 - 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.

AB - 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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U2 - 10.1515/CRELLE.2008.025

DO - 10.1515/CRELLE.2008.025

M3 - Article

AN - SCOPUS:45149102148

SP - 27

EP - 65

JO - Journal fur die Reine und Angewandte Mathematik

JF - Journal fur die Reine und Angewandte Mathematik

SN - 0075-4102

IS - 617

ER -