|
|||||
 |
|
|
|
|
|
|
Shift equivalences
through the lens of Cuntz–Krieger algebras
Toke Meier Carlsen, Adam Dor-On and Søren Eilers |
|
Vol. 17 (2024), No. 1, 345–377
|
 |
Abstract |
|
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. |
Keywords
shift equivalence, Williams' problem, Cuntz–Krieger
algebras, Cuntz–Pimsner algebras, compatible shift
equivalence, Pimsner dilations
|
Mathematical Subject Classification
Primary: 37A55, 46L55
Secondary: 37B10, 37A35, 46L08, 46L35
|
Milestones
Received: 10 March 2022
Revised: 8 August 2022
Accepted: 15 September 2022
Published: 5 February 2024
|
Authors |
| Toke Meier Carlsen | |
| Department of Mathematics University of the Faroe Islands Tórshavn Faroe Islands |
|
| Adam Dor-On | |
| Mathematisches Institut WWU Münster Münster Germany |
|
| Søren Eilers | |
| Department of Mathematical
Sciences University of Copenhagen Copenhagen Denmark |
|
| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
Open Access made possible by participating institutions via Subscribe to Open.
