SHIFT EQUIVALENCES THROUGH THE LENS OF CUNTZ–KRIEGER ALGEBRAS
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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
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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