A dynamical characterization of diagonal-preserving -isomorphisms of graph -algebras
We characterize when there exists a diagonal-preserving $\ast$ -isomorphism between two graph $C^{\ast }$ -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 $E$ and $F$ and...
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| Veröffentlicht in: | Ergodic theory and dynamical systems 2018-10, Vol.38 (7), p.2401-2421 |
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| container_issue | 7 |
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| container_title | Ergodic theory and dynamical systems |
| container_volume | 38 |
| creator | ARKLINT, SARA E. EILERS, SØREN RUIZ, EFREN |
| description | We characterize when there exists a diagonal-preserving
$\ast$
-isomorphism between two graph
$C^{\ast }$
-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
$E$
and
$F$
and show that this is a necessary and sufficient condition for the existence of a diagonal-preserving
$\ast$
-isomorphism between the graph
$C^{\ast }$
-algebras
$C^{\ast }(E)$
and
$C^{\ast }(F)$
. |
| doi_str_mv | 10.1017/etds.2016.141 |
| format | Article |
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$\ast$
-isomorphism between two graph
$C^{\ast }$
-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
$E$
and
$F$
and show that this is a necessary and sufficient condition for the existence of a diagonal-preserving
$\ast$
-isomorphism between the graph
$C^{\ast }$
-algebras
$C^{\ast }(E)$
and
$C^{\ast }(F)$
.</description><identifier>ISSN: 0143-3857</identifier><identifier>EISSN: 1469-4417</identifier><identifier>DOI: 10.1017/etds.2016.141</identifier><language>eng</language><publisher>Cambridge: Cambridge University Press</publisher><subject>Algebra ; Graph theory ; Isomorphism</subject><ispartof>Ergodic theory and dynamical systems, 2018-10, Vol.38 (7), p.2401-2421</ispartof><rights>Cambridge University Press, 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c1765-9eb7267180f6544980f2d4761511fe67bc18537ca5345c4f055d3ae698b5eb023</citedby><cites>FETCH-LOGICAL-c1765-9eb7267180f6544980f2d4761511fe67bc18537ca5345c4f055d3ae698b5eb023</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>ARKLINT, SARA E.</creatorcontrib><creatorcontrib>EILERS, SØREN</creatorcontrib><creatorcontrib>RUIZ, EFREN</creatorcontrib><title>A dynamical characterization of diagonal-preserving -isomorphisms of graph -algebras</title><title>Ergodic theory and dynamical systems</title><description>We characterize when there exists a diagonal-preserving
$\ast$
-isomorphism between two graph
$C^{\ast }$
-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
$E$
and
$F$
and show that this is a necessary and sufficient condition for the existence of a diagonal-preserving
$\ast$
-isomorphism between the graph
$C^{\ast }$
-algebras
$C^{\ast }(E)$
and
$C^{\ast }(F)$
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$\ast$
-isomorphism between two graph
$C^{\ast }$
-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
$E$
and
$F$
and show that this is a necessary and sufficient condition for the existence of a diagonal-preserving
$\ast$
-isomorphism between the graph
$C^{\ast }$
-algebras
$C^{\ast }(E)$
and
$C^{\ast }(F)$
.</abstract><cop>Cambridge</cop><pub>Cambridge University Press</pub><doi>10.1017/etds.2016.141</doi><tpages>21</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0143-3857 |
| ispartof | Ergodic theory and dynamical systems, 2018-10, Vol.38 (7), p.2401-2421 |
| issn | 0143-3857 1469-4417 |
| language | eng |
| recordid | cdi_proquest_journals_2092569115 |
| source | Cambridge University Press Journals Complete |
| subjects | Algebra Graph theory Isomorphism |
| title | A dynamical characterization of diagonal-preserving -isomorphisms of graph -algebras |
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