Self-similar graphs, a unified treatment of Katsura and Nekrashevych C*-algebras
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We study a family of C*-algebras generalizing both Katsura algebras and certain algebras introduced by Nekrashevych in terms of self-similar groups. For these new algebras, we obtain pictures as Cuntz-Pimsner algebras, as well as groupoid C*-algebras. We apply these pictures to characterize simplicity for these algebras, among others.
SubjectsKirchberg algebra; Katsura algebra; Nekrashevych algebra; tight representation; inverse semigroup; groupoid; groupoid C*-algebra
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