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Abstract
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We extend and strengthen a theorem of Bates that says that row-finite graphs that are strong
shift equivalent have Morita equivalent graph C*-algebras. This allows us to ask whether our
stronger notion of Morita equivalence does in fact characterise strong shift equivalence. We
believe this will be relevant for future research on infinite graphs and their C*-algebras. We
also study in-splits and out-splits as particular examples of strong shift equivalences and show
that the induced Morita equivalences respect a whole family of weighted gauge actions. We
then ask whether strong shift equivalence is generated by (generalised) in-splits and out-splits.
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Keywords
strong shift equivalence, graphs, C*-algebras
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Mathematical Subject Classification
Primary: 37A55
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Milestones
Received: 11 December 2022
Accepted: 2 March 2023
Published: 20 May 2024
Communicated by David Royal Larson
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© 2024 The Author(s), under
exclusive license to MSP (Mathematical Sciences
Publishers). |
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