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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Classification of Cuntz-Krieger algebras by orbit equivalence of topological Markov shifts


Author: Kengo Matsumoto
Journal: Proc. Amer. Math. Soc. 141 (2013), 2329-2342
MSC (2010): Primary 46L55; Secondary 46L35, 37B10
Published electronically: March 4, 2013
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Abstract: Let $ A, B$ be square irreducible matrices with entries in $ \{0,1 \}$. Assume that the determinants of $ 1-A$ and $ 1-B$ have the same sign. We will show that the Cuntz-Krieger algebras $ {\mathcal O}_A$ and $ {\mathcal O}_B$ are isomorphic if and only if the right one-sided topological Markov shifts $ (X_A,\sigma _A)$ and $ (X_B,\sigma _B)$ are continuously orbit equivalent.


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Additional Information

Kengo Matsumoto
Affiliation: Department of Mathematics, Joetsu University of Education, Joetsu, 943-8512, Japan
Email: kengo@juen.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11519-4
PII: S 0002-9939(2013)11519-4
Keywords: Cuntz–Krieger algebras, topological Markov shifts, orbit equivalence, $K$-theory, flow equivalence
Received by editor(s): July 13, 2011
Received by editor(s) in revised form: October 12, 2011
Published electronically: March 4, 2013
Communicated by: Bryna Kra
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.