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

Tsuyoshi Kajiwara, Yasuo Watatani

Research output: Contribution to journalArticle

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

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C*-algebra
Self-similar Set
Branch Point
Matrix Representation
Intersection
Singularity
If and only if
Closed
Subset
Coefficient

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Ideals of the core of C*-algebras associated with self-similar maps. / Kajiwara, Tsuyoshi; Watatani, Yasuo.

In: Journal of Operator Theory, Vol. 75, No. 1, 2016, p. 225-255.

Research output: Contribution to journalArticle

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