A dynamical characterization of diagonal-preserving *-isomorphisms of graph C*-algebras

Sara Arklint; Søren Eilers; Efren Ruiz

doi:10.1017/etds.2016.141

A dynamical characterization of diagonal-preserving -isomorphisms of graph C-algebras

Sara Arklint^*, Søren Eilers, Efren Ruiz

^*Corresponding author for this work

Department of Mathematical Sciences

Research output: Contribution to journal › Journal article › Research › peer-review

11 Citations (Scopus)

Abstract

We characterize when there exists a diagonal-preserving (Formula presented.)-isomorphism between two graph (Formula presented.)-algebras in terms of the dynamics of the boundary path spaces. In particular, we refine the notion of ‘orbit equivalence’ between the boundary path spaces of the directed graphs (Formula presented.) and (Formula presented.) and show that this is a necessary and sufficient condition for the existence of a diagonal-preserving (Formula presented.)-isomorphism between the graph (Formula presented.)-algebras (Formula presented.) and (Formula presented.).

Original language	English
Journal	Ergodic Theory and Dynamical Systems
Volume	38
Pages (from-to)	2401-2421
ISSN	0143-3857
DOIs	https://doi.org/10.1017/etds.2016.141
Publication status	Published - 1 Oct 2018

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10.1017/etds.2016.141

Cite this

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title = "A dynamical characterization of diagonal-preserving *-isomorphisms of graph C*-algebras",

abstract = "We characterize when there exists a diagonal-preserving (Formula presented.)-isomorphism between two graph (Formula presented.)-algebras in terms of the dynamics of the boundary path spaces. In particular, we refine the notion of {\textquoteleft}orbit equivalence{\textquoteright} between the boundary path spaces of the directed graphs (Formula presented.) and (Formula presented.) and show that this is a necessary and sufficient condition for the existence of a diagonal-preserving (Formula presented.)-isomorphism between the graph (Formula presented.)-algebras (Formula presented.) and (Formula presented.).",

author = "Sara Arklint and S{\o}ren Eilers and Efren Ruiz",

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language = "English",

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journal = "Ergodic Theory and Dynamical Systems",

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T1 - A dynamical characterization of diagonal-preserving *-isomorphisms of graph C*-algebras

AU - Arklint, Sara

AU - Eilers, Søren

AU - Ruiz, Efren

PY - 2018/10/1

Y1 - 2018/10/1

N2 - We characterize when there exists a diagonal-preserving (Formula presented.)-isomorphism between two graph (Formula presented.)-algebras in terms of the dynamics of the boundary path spaces. In particular, we refine the notion of ‘orbit equivalence’ between the boundary path spaces of the directed graphs (Formula presented.) and (Formula presented.) and show that this is a necessary and sufficient condition for the existence of a diagonal-preserving (Formula presented.)-isomorphism between the graph (Formula presented.)-algebras (Formula presented.) and (Formula presented.).

AB - We characterize when there exists a diagonal-preserving (Formula presented.)-isomorphism between two graph (Formula presented.)-algebras in terms of the dynamics of the boundary path spaces. In particular, we refine the notion of ‘orbit equivalence’ between the boundary path spaces of the directed graphs (Formula presented.) and (Formula presented.) and show that this is a necessary and sufficient condition for the existence of a diagonal-preserving (Formula presented.)-isomorphism between the graph (Formula presented.)-algebras (Formula presented.) and (Formula presented.).

U2 - 10.1017/etds.2016.141

DO - 10.1017/etds.2016.141

M3 - Journal article

AN - SCOPUS:85018457211

SN - 0143-3857

VL - 38

SP - 2401

EP - 2421

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

ER -