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

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

2009-06-10

arxiv.org/abs/0906.1994v2

Mathematics

Operator Algebras

18 pages, 1 figure, Version 2 Comments: Minor changes and a few small typos corrected

Scientific paper

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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