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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

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Volume 2008, Issue 617


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

Takeshi Katsura
  • Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo, 060-0810, Japan. e-mail: katsura@math.sci.hokudai.ac.jp
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Published Online: 2008-05-13 | DOI: https://doi.org/10.1515/CRELLE.2008.025


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.

About the article

Received: 2006-08-11

Revised: 2007-01-17

Published Online: 2008-05-13

Published in Print: 2008-04-01

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2008, Issue 617, Pages 27–65, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/CRELLE.2008.025.

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