Shift equivalences through the lens of Cuntz-Krieger algebras
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _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 |