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

Tsuyoshi Kajiwara; Yasuo Watatani

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arXiv · 1306.1878

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

Tsuyoshi Kajiwara·Yasuo Watatani

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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.

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Tsuyoshi Kajiwara, Yasuo Watatani. 2013-06-08. Ideals of the core of C*-algebras associated with self-similar maps. https://arxiv.org/abs/1306.1878

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