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

Shinji Yamashita

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

Operator Algebras 2009-06-18 v2

Authors: Shinji Yamashita

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 $\mathbb{N}$ .

Keywords

Cuntz-Krieger uniqueness theorem product system C*-algebras topological higher-rank graphs simplicity purely infiniteness ax+b-semigroup C*-algebra

Cite

@article{arxiv.0906.1994,
  title  = {Cuntz's $ax+b$-semigroup C*-algebra over $\mathbb{N}$ and product system C*-algebras},
  author = {Shinji Yamashita},
  journal= {arXiv preprint arXiv:0906.1994},
  year   = {2009}
}

Comments

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