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

Brix, Kevin Aguyar; Gautam, Pete

doi:10.2140/involve.2024.17.293

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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

DOI: 10.2140/involve.2024.17.293

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

Vol. 17, No. 2, 2024