C*-algebras associated with self-similar sets

Tsuyoshi Kajiwara, Yasuo Watatani

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

Let γ = (γ1,..., γN), N ≥ 2, be a system of proper contractions on a complete metric space. Then there exists a unique self-similar non-empty compact subset K. We consider the union G = ∪i=1N {(x,y) ∈ K2;x = γi(y)} of the cographs of γi. Then X = C(G) is a Hilbert bimodule over A = C(K). We associate a C*-algebra script O signγ(K) with them as a Cuntz-Pimsner algebra script O signX. We show that if a system of proper contractions satisfies the open set condition in K, then the C*-algebra script O sign γ(K) is simple, purely infinite and, in general, not isomorphic to a Cuntz algebra.

Original languageEnglish
Pages (from-to)225-247
Number of pages23
JournalJournal of Operator Theory
Volume56
Issue number2
Publication statusPublished - Sep 1 2006

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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    Kajiwara, T., & Watatani, Y. (2006). C*-algebras associated with self-similar sets. Journal of Operator Theory, 56(2), 225-247.