Shift equivalences through the lens of Cuntz-Krieger algebras

Fuente: arXiv
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Main Authors: Carlsen, Toke Meier, Dor-On, Adam, Eilers, Søren
Format: Preprint
Published: 2020
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_version_ 1866911775714181120
author Carlsen, Toke Meier
Dor-On, Adam
Eilers, Søren
author_facet Carlsen, Toke Meier
Dor-On, Adam
Eilers, Søren
contents Motivated by Williams' problem of measuring novel differences between shift equivalence (SE) and strong shift equivalence (SSE), we introduce three equivalence relations that provide new ways to obstruct SSE while merely assuming SE. Our shift equivalence relations arise from studying graph C*-algebras, where a variety of intermediary equivalence relations naturally arise. As a consequence we realize a goal sought after by Muhly, Pask and Tomforde, measure a delicate difference between SSE and SE in terms of Pimsner dilations for C*-correspondences of adjacency matrices, and use this distinction to refute a proof from a previous paper.
format Preprint
id arxiv_https___arxiv_org_abs_2011_10320
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Shift equivalences through the lens of Cuntz-Krieger algebras
Carlsen, Toke Meier
Dor-On, Adam
Eilers, Søren
Operator Algebras
Dynamical Systems
Primary: 37A55, 46L55 Secondary: 37B10, 37A35, 46L08, 46L35, 54H20
Motivated by Williams' problem of measuring novel differences between shift equivalence (SE) and strong shift equivalence (SSE), we introduce three equivalence relations that provide new ways to obstruct SSE while merely assuming SE. Our shift equivalence relations arise from studying graph C*-algebras, where a variety of intermediary equivalence relations naturally arise. As a consequence we realize a goal sought after by Muhly, Pask and Tomforde, measure a delicate difference between SSE and SE in terms of Pimsner dilations for C*-correspondences of adjacency matrices, and use this distinction to refute a proof from a previous paper.
title Shift equivalences through the lens of Cuntz-Krieger algebras
topic Operator Algebras
Dynamical Systems
Primary: 37A55, 46L55 Secondary: 37B10, 37A35, 46L08, 46L35, 54H20
url https://arxiv.org/abs/2011.10320