On strong shift equivalence for row-finite graphs and C*-algebras
(2024) In Involve 17(2). p.293-309- Abstract
We extend and strengthen a theorem of Bates that says that row-finite graphs that are strong shift equivalent have Morita equivalent graph C*-algebras. This allows us to ask whether our stronger notion of Morita equivalence does in fact characterise strong shift equivalence. We believe this will be relevant for future research on infinite graphs and their C*-algebras. We also study in-splits and out-splits as particular examples of strong shift equivalences and show that the induced Morita equivalences respect a whole family of weighted gauge actions. We then ask whether strong shift equivalence is generated by (generalised) in-splits and out-splits.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/c816fe27-4371-46f3-bb22-4ad087b73fff
- author
- Brix, Kevin Aguyar LU and Gautam, Pete
- organization
- publishing date
- 2024-05-01
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- C*-algebras, graphs, strong shift equivalence
- in
- Involve
- volume
- 17
- issue
- 2
- pages
- 17 pages
- publisher
- Mathematical Sciences Publishers
- external identifiers
-
- scopus:85194853404
- ISSN
- 1944-4176
- DOI
- 10.2140/involve.2024.17.293
- language
- English
- LU publication?
- yes
- id
- c816fe27-4371-46f3-bb22-4ad087b73fff
- date added to LUP
- 2024-09-04 11:10:11
- date last changed
- 2024-09-04 11:10:40
@article{c816fe27-4371-46f3-bb22-4ad087b73fff, abstract = {{<p>We extend and strengthen a theorem of Bates that says that row-finite graphs that are strong shift equivalent have Morita equivalent graph C*-algebras. This allows us to ask whether our stronger notion of Morita equivalence does in fact characterise strong shift equivalence. We believe this will be relevant for future research on infinite graphs and their C*-algebras. We also study in-splits and out-splits as particular examples of strong shift equivalences and show that the induced Morita equivalences respect a whole family of weighted gauge actions. We then ask whether strong shift equivalence is generated by (generalised) in-splits and out-splits.</p>}}, author = {{Brix, Kevin Aguyar and Gautam, Pete}}, issn = {{1944-4176}}, keywords = {{C*-algebras; graphs; strong shift equivalence}}, language = {{eng}}, month = {{05}}, number = {{2}}, pages = {{293--309}}, publisher = {{Mathematical Sciences Publishers}}, series = {{Involve}}, title = {{On strong shift equivalence for row-finite graphs and C*-algebras}}, url = {{http://dx.doi.org/10.2140/involve.2024.17.293}}, doi = {{10.2140/involve.2024.17.293}}, volume = {{17}}, year = {{2024}}, }