Diagonal-preserving gauge-invariant isomorphisms of graph $C^*$-algebras

Toke Meier Carlsen; James Rout

doi:10.1016/j.jfa.2017.06.018

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arXiv · 1610.00692

Diagonal-preserving gauge-invariant isomorphisms of graph $C^*$-algebras

Toke Meier Carlsen·James Rout

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Abstract

We study graph $C^*$-algebras equipped with generalised gauge actions, and characterise in terms of groupoids and groupoid cocycles when two graph $C^*$-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.

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BibTeX RIS

Toke Meier Carlsen, James Rout. 2016-10-03. Diagonal-preserving gauge-invariant isomorphisms of graph $C^*$-algebras. https://doi.org/10.1016/j.jfa.2017.06.018

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