Article contents
A dynamical characterization of diagonal-preserving
$^{\ast }$-isomorphisms of graph
$C^{\ast }$-algebras
Published online by Cambridge University Press: 02 May 2017
Abstract
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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- Original Article
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- © Cambridge University Press, 2017
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