Diagonal-preserving gauge-invariant isomorphisms of graph $C^{\ast }$-algebras

Abstract

We study graph $C^{\ast }$-algebras equipped with generalised gauge actions, and characterise in terms of groupoids and groupoid cocycles when two graph $C^{\ast }$-algebras are isomorphic by a diagonal-preserving isomorphism that intertwines the generalised gauge actions. We apply this characterisation to show that two Cuntz-Krieger algebras are isomorphic by a diagonal-preserving isomorphism that intertwines the gauge actions if and only if the corresponding one-sided subshifts are eventually conjugate, and that the stabilisation of two Cuntz-Krieger algebras are isomorphic by a diagonal-preserving isomorphism that intertwines the gauge actions if and only if the corresponding two-sided subshifts are conjugate.

arXiv comment12 pages

References in corpus (6)

• Continuous orbit equivalence of topological Markov shifts and Cuntz-Krieger algebras
• Equivalence and stable isomorphism of groupoids, and diagonal-preserving stable isomorphisms of graph C*-algebras and Leavitt path algebras
• The Path Space of a Directed Graph
• Graph algebras and orbit equivalence
• Stability of C*-algebras associated to graphs
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Cited by in corpus (16)

• Reconstruction of groupoids and C*-rigidity of dynamical systems
• Orbit equivalence of graphs and isomorphism of graph groupoids
• Cuntz-Krieger algebras and one-sided conjugacy of shifts of finite type and their groupoids
• Conjugacy of local homeomorphisms via groupoids and C*-algebras
• C*-algebras, groupoids and covers of shift spaces
• Shift equivalences through the lens of Cuntz-Krieger algebras
• Refined moves for structure-preserving isomorphism of graph C*-algebras
• Orbit equivalence of higher-rank graphs
• Splittings for C*-correspondences and strong shift equivalence
• One-sided topological conjugacy of normal subshifts and gauge actions on the associated $C^{\ast }$-algebras
• On one-sided topological conjugacy of topological Markov shifts and gauge actions on Cuntz--Krieger algebras
• Continuous orbit equivalence for automorphismhi systems of equivalence relations
• On strong shift equivalence for row-finite graphs and C*-algebras
• An étale equivalence relation on a configuration space arising from a subshift and related $C^{\ast }$-algebras
• Asymptotic continuous orbit equivalence of Smale spaces and Ruelle algebras
• $C^{\ast }$-rigidity of dynamical systems and étale groupoids