Journal of Operator Theory
Volume 74, Issue 2, Fall 2015 pp. 457-483.
Strongly continuous orbit equivalence of
one-sided topological Markov shifts
Authors:
Kengo Matsumoto
Author institution: Department of Mathematics,
Joetsu University of Education,
Joetsu, 943-8512, Japan
Summary: We prove that
one-sided topological Markov shifts
$(X_A, \sigma_A)$
and
$(X_B, \sigma_B)$
are strongly continuous orbit equivalent
if and only if
there exists an isomorphism between
the Cuntz--Krieger algebras
${\mathcal{O}}_A$ and
${\mathcal{O}}_B$
preserving their maximal commutative $C^*$-subalgebras
$C(X_A)$ and $C(X_B)$
and giving cocycle conjugate gauge actions.
An example of one-sided topological
Markov shifts which are
strongly continuous orbit equivalent
but not one-sided topologically conjugate
is presented.
DOI: http://dx.doi.org/10.7900/jot.2014aug19.2063
Keywords: Cuntz-Krieger algebras, gauge action,
topological Markov shifts, orbit equivalence
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