Abstract
We study KMS states for gauge actions with potential functions on Cuntz--Krieger algebras whose underlying one-sided topological Markov shifts are continuous orbit equivalent. As a result, we have a certain relationship between topological entropy of continuous orbit equivalent one-sided topological Markov shifts.
Highlights
Let A = [A(i, j)]Ni,j=1 be a square matrix with entries in {0, 1}, where 1 < N ∈ N
The two-sided topological Markov shift (XA, σA) is a topological dynamical system of a homeomorphism σA((xn)n∈Z)) =n∈Z on the zero-dimensional compact Hausdorff space XA consisting of two-sided sequencesn∈Z
For f ∈ Fθ(XA), there exists a unique positive real number βf ∈ R such that there exists a log βf -KMS state for the γf -action on OA
Summary
Let us denote by DA the C∗-subalgebra of OA generated by the projections of the form Sμ1 · · · Sμn Sμ∗n · · · Sμ∗1 for μ1 · · · μn ∈ B∗(XA) It is well-known that the commutative C∗-algebra C(XA) of complex valued continuous functions on XA is regarded as the C∗-. In [13], the author studied generalized gauge actions from the viewpoints of continuous orbit equivalence and flow equivalence of topological Markov shifts In [13], a notion of strongly continuous orbit equivalence between one-sided topological Markov shifts (XA, σA) and (XB, σB) was introduced It is defined as the cases where the cocycle function c1 is cohomologous to 1 in C(XA, Z). 1 0 for which (XA, σA) and (XB, σB) are continuously orbit equivalent
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