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On strong shift equivalence for row-finite graphs and C*-algebras

Brix, Kevin Aguyar LU and Gautam, Pete (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.

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author
and
organization
publishing date
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
2025-04-04 15:11:19
@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}},
}