C*-algebras and self-similar groups Academic Article uri icon

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. 2009 Walter de Gruyter Berlin, New York.

published proceedings

  • Journal fr die reine und angewandte Mathematik (Crelles Journal)

author list (cited authors)

  • Nekrashevych, V.

citation count

  • 36

complete list of authors

  • Nekrashevych, Volodymyr

publication date

  • January 2009