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.
Original language | English |
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Pages (from-to) | 345-377 |
Number of pages | 33 |
Journal | Analysis and PDE |
Volume | 17 |
Issue number | 1 |
DOIs | |
State | Published - 2024 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2024 MSP (Mathematical Sciences Publishers).
Keywords
- Cuntz–Krieger algebras
- Cuntz–Pimsner algebras
- Pimsner dilations
- Williams’ problem
- compatible shift equivalence
- shift equivalence
ASJC Scopus subject areas
- Analysis
- Numerical Analysis
- Applied Mathematics