C*-algebras associated with self-similar sets

Tsuyoshi Kajiwara, Yasuo Watatani

    Research output: Contribution to journalArticlepeer-review

    12 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 - Sept 2006

    All Science Journal Classification (ASJC) codes

    • Algebra and Number Theory

    Fingerprint

    Dive into the research topics of 'C*-algebras associated with self-similar sets'. Together they form a unique fingerprint.

    Cite this