Corners of Cuntz-Krieger algebras
Abstract
We show that if $A$ is a unital $C^*$-algebra and $B$ is a Cuntz-Krieger algebra for which $A\otimes\mathbb{K} \cong B\otimes\mathbb{K}$, then $A$ is a Cuntz-Krieger algebra. Consequently, corners of Cuntz-Krieger algebras are Cuntz-Krieger algebras.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2012
- DOI:
- 10.48550/arXiv.1209.4336
- arXiv:
- arXiv:1209.4336
- Bibcode:
- 2012arXiv1209.4336A
- Keywords:
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- Mathematics - Operator Algebras;
- 46L55
- E-Print:
- Version 3: 20 pages. Corrected typos and added or clarified definitions. This is the version that will be published. Version 2: 18 pages, removed unnecessary assumptions in Theorem 3.5 and Corollary 3.6, and updated references