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

DOI10.1215/21562261-2801849zbMath1320.46055arXiv1403.0719OpenAlexW2068258253MaRDI QIDQ482154

Hiroki Matui, Kengo Matsumoto

Publication date: 19 December 2014

Published in: Kyoto Journal of Mathematics, Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.0719

zbMATH Keywords

Borel measureperiodic pointMarkov shiftsCuntz-Krieger algebrasMarkov shiftorbit equivalentcocycle function

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55) Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Symbolic dynamics (37B10) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30) Dynamical systems and the theory of (C^*)-algebras (37A55)

Related Items (52)

TWISTS, CROSSED PRODUCTS AND INVERSE SEMIGROUP COHOMOLOGY ⋮ Reconstruction of groupoids and \(C^\ast \)-rigidity of dynamical systems ⋮ On a family of C*-subalgebras of Cuntz–Krieger algebras ⋮ Diagonal-preserving isomorphisms of étale groupoid algebras ⋮ The Cuntz splice does not preserve \(\ast\)-isomorphism of Leavitt path algebras over \(\mathbb{Z}\) ⋮ Uniformly continuous orbit equivalence of Markov shifts and gauge actions on Cuntz–Krieger algebras ⋮ Étale groupoids arising from products of shifts of finite type ⋮ A short note on Cuntz splice from a viewpoint of continuous orbit equivalence of topological Markov shifts ⋮ Continuous cocycle superrigidity for shifts and groups with one end ⋮ Diagonal-preserving gauge-invariant isomorphisms of graph \(C^{\ast}\)-algebras ⋮ On one-sided topological conjugacy of topological Markov shifts and gauge actions on Cuntz–Krieger algebras ⋮ Reconstruction of graded groupoids from graded Steinberg algebras ⋮ Amplified graph C*-algebras II: Reconstruction ⋮ Relative Morita equivalence of Cuntz–Krieger algebras and flow equivalence of topological Markov shifts ⋮ Topological conjugacy of topological Markov shifts and Cuntz-Krieger algebras ⋮ Cartan subalgebras for non-principal twisted groupoid \(C^\ast\)-algebras ⋮ One-sided topological conjugacy of topological Markov shifts, continuous full groups and Cuntz–Krieger algebras ⋮ Uniform enveloping semigroupoids for groupoid actions ⋮ Equivalence and stable isomorphism of groupoids, and diagonal-preserving stable isomorphisms of graph 𝐶*-algebras and Leavitt path algebras ⋮ \(\mathrm{C}^\ast\)-algebras. Abstracts from the workshop held August 7--13, 2022 ⋮ Continuous orbit equivalence for automorphism systems of equivalence relations ⋮ Continuous orbit equivalence of topological Markov shifts and KMS states on Cuntz-Krieger algebras ⋮ Conjugacy of local homeomorphisms via groupoids and C*-algebras ⋮ Shift equivalences through the lens of Cuntz-Krieger algebras ⋮ Graph algebras and orbit equivalence ⋮ Subgroups of continuous full groups and relative continuous orbit equivalences of one-sided topological Markov shifts ⋮ The mapping class group of a shift of finite type ⋮ Topological full groups of ample groupoids with applications to graph algebras ⋮ Coded equivalence of one-sided topological Markov shifts ⋮ Graded \(C^*\)-algebras and twisted groupoid \(C^*\)-algebras ⋮ 𝐶*-algebras, groupoids and covers of shift spaces ⋮ CUNTZ–KRIEGER ALGEBRAS AND ONE-SIDED CONJUGACY OF SHIFTS OF FINITE TYPE AND THEIR GROUPOIDS ⋮ Toeplitz quotient \(C^*\)-algebras and ratio limits for random walks ⋮ Continuous orbit equivalence rigidity ⋮ Continuous orbit equivalence, flow equivalence of Markov shifts and circle actions on Cuntz-Krieger algebras ⋮ \(C^\ast\)-algebras associated to Boolean dynamical systems ⋮ Maximal abelian subalgebras of \(C^\ast\)-algebras associated with complex dynamical systems and self-similar maps ⋮ A dynamical characterization of diagonal-preserving -isomorphisms of graph -algebras ⋮ Asymptotic Continuous Orbit Equivalence of Smale Spaces and Ruelle Algebras ⋮ The homology of the Katsura-Exel-Pardo groupoid ⋮ On flow equivalence of one-sided topological Markov shifts ⋮ Flow equivalence and orbit equivalence for shifts of finite type and isomorphism of their groupoids ⋮ Balanced strong shift equivalence, balanced in-splits, and eventual conjugacy ⋮ A groupoid approach toC*-algebras associated withλ-graph systems and continuous orbit equivalence of subshifts ⋮ Cohomology groups, continuous full groups and continuous orbit equivalence of topological Markov shifts ⋮ Flow equivalence of topological Markov shifts and Ruelle algebras ⋮ ORBIT EQUIVALENCE ON SELF-SIMILAR GROUPS AND THEIR C*-ALGEBRAS ⋮ On certain inverse semigroups associated with one-sided topological Markov shifts ⋮ The dynamics of partial inverse semigroup actions ⋮ Full groups of one-sided topological Markov shifts ⋮ One-sided topological conjugacy of normal subshifts and gauge actions on the associatedC*-algebras ⋮ Topological Full Groups of Étale Groupoids

Cites Work

• Orbit equivalence of topological Markov shifts and Cuntz-Krieger algebras
• A groupoid approach to C*-algebras
• A class of C*-algebras and topological Markov chains
• A topological invariant of flows on 1-dimensional spaces
• Orbit equivalence, flow equivalence and ordered cohomology
• Classification of Cuntz-Krieger algebras
• Classification of Cuntz–Krieger algebras by orbit equivalence of topological Markov shifts
• Homology and topological full groups of étale groupoids on totally disconnected spaces
• An Introduction to Symbolic Dynamics and Coding
• Meromorphic extensions of a class of dynamical zeta functions and their special values at the origin

This page was built for publication: Continuous orbit equivalence of topological Markov shifts and Cuntz-Krieger algebras