Ideals of the core of C*-algebras associated with self-similar maps

Tsuyoshi Kajiwara, Yasuo Watatani

    Research output: Contribution to journalArticlepeer-review

    1 Citation (Scopus)

    Abstract

    We give a complete classification of the ideals of the core of the C*-algebras associated with self-similar maps under a certain condition. Any ideal is completely determined by the intersection with the coefficient algebra C(K) of the self-similar set K. The corresponding closed subset of K is described by the singularity structure of the self-similar map. In particular the core is simple if and only if the self-similar map has no branch point. A matrix representation of the core is essentially used to prove the classification.

    Original languageEnglish
    Pages (from-to)225-255
    Number of pages31
    JournalJournal of Operator Theory
    Volume75
    Issue number1
    DOIs
    Publication statusPublished - 2016

    Keywords

    • C*-correspondences
    • Core
    • Ideals
    • Self-similar maps

    ASJC Scopus subject areas

    • Algebra and Number Theory

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