SHIFT EQUIVALENCES THROUGH THE LENS OF CUNTZ–KRIEGER ALGEBRAS

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

SHIFT EQUIVALENCES THROUGH THE LENS OF CUNTZ–KRIEGER ALGEBRAS. / Carlsen, Toke Meier; Dor-On, Adam; Eilers, Søren.

In: Analysis and PDE, Vol. 17, No. 1, 2024, p. 345-377.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Carlsen, TM, Dor-On, A & Eilers, S 2024, 'SHIFT EQUIVALENCES THROUGH THE LENS OF CUNTZ–KRIEGER ALGEBRAS', Analysis and PDE, vol. 17, no. 1, pp. 345-377. https://doi.org/10.2140/apde.2024.17.345

APA

Carlsen, T. M., Dor-On, A., & Eilers, S. (2024). SHIFT EQUIVALENCES THROUGH THE LENS OF CUNTZ–KRIEGER ALGEBRAS. Analysis and PDE, 17(1), 345-377. https://doi.org/10.2140/apde.2024.17.345

Vancouver

Carlsen TM, Dor-On A, Eilers S. SHIFT EQUIVALENCES THROUGH THE LENS OF CUNTZ–KRIEGER ALGEBRAS. Analysis and PDE. 2024;17(1):345-377. https://doi.org/10.2140/apde.2024.17.345

Author

Carlsen, Toke Meier ; Dor-On, Adam ; Eilers, Søren. / SHIFT EQUIVALENCES THROUGH THE LENS OF CUNTZ–KRIEGER ALGEBRAS. In: Analysis and PDE. 2024 ; Vol. 17, No. 1. pp. 345-377.

Bibtex

@article{d89a7f44451f42da9deeca5af95f35c9,
title = "SHIFT EQUIVALENCES THROUGH THE LENS OF CUNTZ–KRIEGER ALGEBRAS",
abstract = "Motivated by Williams{\textquoteright} 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 = "compatible shift equivalence, Cuntz–Krieger algebras, Cuntz–Pimsner algebras, Pimsner dilations, shift equivalence, Williams{\textquoteright} problem",
author = "Carlsen, {Toke Meier} and Adam Dor-On and S{\o}ren Eilers",
note = "Publisher Copyright: {\textcopyright} 2024 MSP (Mathematical Sciences Publishers).",
year = "2024",
doi = "10.2140/apde.2024.17.345",
language = "English",
volume = "17",
pages = "345--377",
journal = "Analysis and PDE",
issn = "2157-5045",
publisher = "Mathematical Sciences Publishers",
number = "1",

}

RIS

TY - JOUR

T1 - SHIFT EQUIVALENCES THROUGH THE LENS OF CUNTZ–KRIEGER ALGEBRAS

AU - Carlsen, Toke Meier

AU - Dor-On, Adam

AU - Eilers, Søren

N1 - Publisher Copyright: © 2024 MSP (Mathematical Sciences Publishers).

PY - 2024

Y1 - 2024

N2 - 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.

AB - 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.

KW - compatible shift equivalence

KW - Cuntz–Krieger algebras

KW - Cuntz–Pimsner algebras

KW - Pimsner dilations

KW - shift equivalence

KW - Williams’ problem

U2 - 10.2140/apde.2024.17.345

DO - 10.2140/apde.2024.17.345

M3 - Journal article

AN - SCOPUS:85188447584

VL - 17

SP - 345

EP - 377

JO - Analysis and PDE

JF - Analysis and PDE

SN - 2157-5045

IS - 1

ER -

ID: 388679201