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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 2009, Issue 630


C*-algebras and self-similar groups

Volodymyr Nekrashevych
Published Online: 2009-03-31 | DOI: https://doi.org/10.1515/CRELLE.2009.035


We study Cuntz-Pimsner algebras naturally associated with self-similar groups (like iterated monodromy groups of expanding dynamical systems). In particular, we show how to reconstruct the Julia set of an expanding map from the Cuntz-Pimsner algebra of the associated iterated monodromy group and the gauge action on it. We compute K-theory of algebras associated with complex hyperbolic rational functions. It is proved that under some natural conditions the Cuntz-Pimsner algebra of a self-similar group is purely infinite, simple and nuclear. We also show a relation of our algebras with Ruelle algebras of the associated solenoids.

About the article

Received: 2007-08-31

Published Online: 2009-03-31

Published in Print: 2009-05-01

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2009, Issue 630, Pages 59–123, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/CRELLE.2009.035.

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