Splittings for C* -correspondences and strong shift equivalence

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dc.contributor.authorBrix, K.A.
dc.contributor.authorMundey, A.
dc.contributor.authorRennie, A.
dc.date.issued2024
dc.description.abstractWe present an extension of the notion of in-splits from symbolic dynamics to topological graphs and, more generally, to C* -correspondences. We demonstrate that in-splits provide examples of strong shift equivalences of C* -correspondences. Furthermore, we provide a streamlined treatment of Muhly, Pask, and Tomforde's proof that any strong shift equivalence of regular C* -correspondences induces a (gauge-equivariant) Morita equivalence between Cuntz-Pimsner algebras. For topological graphs, we prove that in-splits induce diagonal-preserving gauge-equivariant ∗-isomorphisms in analogy with the results for Cuntz-Krieger algebras. Additionally, we examine the notion of out-splits for C* -correspondences.
dc.description.statementofresponsibilityKevin Aguyar Brix, Alexander Mundey, Adam Rennie
dc.identifier.citationMathematica Scandinavica, 2024; 130(1):101-148
dc.identifier.doi10.7146/math.scand.a-142308
dc.identifier.issn0025-5521
dc.identifier.issn1903-1807
dc.identifier.orcidMundey, A. [0000-0002-7791-4383]
dc.identifier.urihttps://hdl.handle.net/2440/148001
dc.language.isoen
dc.publisherMathematica Scandinavica
dc.relation.granthttp://purl.org/au-research/grants/arc/DP200100155
dc.rights© 2024 Mathematica Scandinavica
dc.source.urihttps://doi.org/10.7146/math.scand.a-142308
dc.titleSplittings for C* -correspondences and strong shift equivalence
dc.typeJournal article
pubs.publication-statusPublished

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