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

2013/06/08 by Tsuyoshi Kajiwara, Kajiwara, Tsuyoshi, Yasuo Watatani +1
Mathematics · #46L08 #46L55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics #math.DS #math.OA #msc:46L08 #msc:46L55

paper · pdf · doi:10.48550/arxiv.1306.1878

LaTeX 2e, 26 pages

arxiv created 2013/06/08 · openalex publication_date 2013/06/08 · arxiv updated 2013/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Ideal structure and simplicity of the C*-algebras generated by Hilbert bimodules

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