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 2006

Fingerprint

Cuntz Algebra
Self-similar Set
C*-algebra
Contraction
Open Set Condition
Cographs
Complete Metric Space
Bimodule
Hilbert
Union
Isomorphic
Subset

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

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

C*-algebras associated with self-similar sets. / Kajiwara, Tsuyoshi; Watatani, Yasuo.

In: Journal of Operator Theory, Vol. 56, No. 2, 09.2006, p. 225-247.

Research output: Contribution to journalArticle

Kajiwara, T & Watatani, Y 2006, 'C*-algebras associated with self-similar sets', Journal of Operator Theory, vol. 56, no. 2, pp. 225-247.
Kajiwara T, Watatani Y. C*-algebras associated with self-similar sets. Journal of Operator Theory. 2006 Sep;56(2):225-247.
Kajiwara, Tsuyoshi ; Watatani, Yasuo. / C*-algebras associated with self-similar sets. In: Journal of Operator Theory. 2006 ; Vol. 56, No. 2. pp. 225-247.
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