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.
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.
UR - http://www.scopus.com/inward/record.url?scp=45149102148&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=45149102148&partnerID=8YFLogxK
U2 - 10.1515/CRELLE.2008.025
DO - 10.1515/CRELLE.2008.025
M3 - Article
AN - SCOPUS:45149102148
SN - 0075-4102
SP - 27
EP - 65
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
IS - 617
ER -