Flow equivalence and orbit equivalence for shifts of finite type and isomorphism of their groupoids

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:469

Article

Carlsen, Toke Meier¹  Eilers, Soren²  Ortega, Eduard³  Restorff, Gunnar¹ 

[1] Univ Faroe Isl, Dept Sci & Technol, Noatun 3, FO-100 Torshavn, Denmark

[2] Univ Copenhagen, Dept Math Sci, Univ Pk 5, DK-2100 Copenhagen, Denmark

[3] NTNU, Dept Math Sci, NO-7491 Trondheim, Norway

关键词: Continuous orbit equivalence;    Flow equivalence;    Etale groupoids;    Graph C*-algebras;    Leavitt path algebras;    Diagonal-preserving isomorphisms;   

DOI  :  10.1016/j.jmaa.2018.09.056

来源: Elsevier

【 摘 要 】

We give conditions for when continuous orbit equivalence of one-sided shift spaces implies flow equivalence of the associated two-sided shift spaces. Using groupoid techniques, we prove that this is always the case for shifts of finite type. This generalises a result of Matsumoto and Matui from the irreducible to the general case. We also prove that a pair of one-sided shift spaces of finite type are continuously orbit equivalent if and only if their groupoids are isomorphic, and that the corresponding two-sided shifts are flow equivalent if and only if the groupoids are stably isomorphic. As applications we show that two finite directed graphs with no sinks and no sources are move equivalent if and only if the corresponding graph C*-algebras are stably isomorphic by a diagonal-preserving isomorphism (if and only if the corresponding Leavitt path algebras are stably isomorphic by a diagonal-preserving isomorphism), and that two topological Markov chains are flow equivalent if and only if there is a diagonal-preserving isomorphism between the stabilisations of the corresponding Cuntz-Krieger algebras (the latter generalises a result of Matsumoto and Matui about irreducible topological Markov chains with no isolated points to a result about general topological Markov chains). We also show that for general shift spaces, strongly continuous orbit equivalence implies two-sided conjugacy. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free