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Licensed Unlicensed Requires Authentication Published by De Gruyter March 31, 2009

C*-algebras and self-similar groups

Volodymyr Nekrashevych
From the journal

Abstract

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.

Received: 2007-08-31
Published Online: 2009-03-31
Published in Print: 2009-May

© Walter de Gruyter Berlin · New York 2009

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