Journal of Operator Theory

Volume 52, Issue 2, Fall 2004 pp. 223-249.

Cuntz-Pimsner algebras of group actions

Authors: Volodymyr V. Nekrashevych
Author institution: International University Bremen, School of Engineering and Science, P.O. Box 750 561, 28725 Bremen, Germany

Summary: We associate a $*$-bimodule over the group algebra to every self-similar group action on the space of one-sided sequences. Completions of the group algebra, which agree with the bimodule are investigated. This gives new examples of Hilbert bimodules and the associated Cuntz-Pimsner algebras. A direct proof of simplicity of these algebras is given. We show also a relation between the Cuntz algebras and the Higman-Thompson groups and define an analog of the Higman-Thompson group for the Cuntz-Pimsner algebra of a self-similar group action.

Keywords: self-similar group actions, one-sided shift, bimodules, Cuntz algebras, Cuntz-Pimsner algebras, Higman-Thompson groups, Grigorchuk group

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