Continuous orbit equivalence, flow equivalence of Markov shifts and circle actions on Cuntz--Krieger algebras

Abstract

We will study torus actions on Cuntz--Krieger algebras trivially acting on its canonical maximal abelian $C^{\ast }$-subalgebras from the view points of continuous orbit equivalence of one-sided topological Markov shifts and flow equivalence of two-sided topological Markov shifts.

22 pages. Title was changed. to appear in Math. Z

References in corpus (1)

• Continuous orbit equivalence of topological Markov shifts and Cuntz-Krieger algebras

Cited by in corpus (4)

• C*-algebras, groupoids and covers of shift spaces
• Uniformly continuous orbit equivalence of Markov shifts and gauge actions on Cuntz-Krieger algebras
• Relative Morita equivalence of Cuntz--Krieger algebras and flow equivalence of topological Markov shifts
• Imprimitivity bimodules of Cuntz--Krieger algebras and strong shift equivalences of matrices