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

Matsumoto, Kengo

doi:10.1090/S0002-9939-2013-11519-4

Classification of Cuntz–Krieger algebras by orbit equivalence of topological Markov shifts
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Proc. Amer. Math. Soc. 141 (2013), 2329-2342 Request permission

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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