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On strong shift equivalence for row-finite graphs and C*-algebras

Kevin Aguyar Brix and Pete Gautam

Vol. 17 (2024), No. 2, 293–309
Abstract

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.

Keywords
strong shift equivalence, graphs, C*-algebras
Mathematical Subject Classification
Primary: 37A55
Milestones
Received: 11 December 2022
Accepted: 2 March 2023
Published: 20 May 2024

Communicated by David Royal Larson
Authors
Kevin Aguyar Brix
Centre for Mathematical Sciences
Lund University
Lund
Sweden
Pete Gautam
School of Mathematics
Birmingham University
Birmingham
United Kingdom