Cuntz's $ax+b$-semigroup C*-algebra over $\mathbb{N}$ and product system C*-algebras

Shinji Yamashita

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arXiv · 0906.1994

Cuntz's $ax+b$-semigroup C-algebra over $\mathbb{N}$ and product system C-algebras

Shinji Yamashita

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Abstract

We investigate $C^*$-algebras associated with row-finite topological higher-rank graphs with no source, which are based on product system $C^*$-algebras. We prove the Cuntz-Krieger uniqueness theorem, and provide the condition of simplicity and purely infiniteness of our algebras. We give examples of non-discrete topological higher-rank graphs whose $C^*$-algebras contain Cuntz's $ax+b$-semigroup $C^*$-algebra over $\mathbb{N}$.

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BibTeX RIS

Shinji Yamashita. 2009-06-18. Cuntz's $ax+b$-semigroup C*-algebra over $\mathbb{N}$ and product system C*-algebras. https://arxiv.org/abs/0906.1994

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