2004
DOI: 10.1017/s0143385703000348
|View full text |Cite
|
Sign up to set email alerts
|

Flow equivalence of graph algebras

Abstract: This paper explores the effect of various graphical constructions upon the associated graph C * -algebras. The graphical constructions in question arise naturally in the study of flow equivalence for topological Markov chains. We prove that outsplittings give rise to isomorphic graph algebras, and in-splittings give rise to strongly Morita equivalent C * -algebras. We generalise the notion of a delay as defined in [D] to form in-delays and out-delays. We prove that these constructions give rise to Morita equiv… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
4
1

Citation Types

1
83
0

Year Published

2006
2006
2017
2017

Publication Types

Select...
3
3

Relationship

0
6

Authors

Journals

citations
Cited by 50 publications
(84 citation statements)
references
References 19 publications
1
83
0
Order By: Relevance
“…After a brief review of the established definitions and notations for graph algebras, we state and prove our main result, Theorem 3.1, which shows that any finite tree is contractible in the above sense, and that a similar construction may be applied to more general acyclic subgraphs. In particular, this theorem combines several of the separate results of [4] and may cover some further examples as well. Our proof follows closely the direct methods of [4], and makes use of a powerful theorem of [3], the gauge-invariant uniqueness theorem.…”
Section: Introductionmentioning
confidence: 65%
See 4 more Smart Citations
“…After a brief review of the established definitions and notations for graph algebras, we state and prove our main result, Theorem 3.1, which shows that any finite tree is contractible in the above sense, and that a similar construction may be applied to more general acyclic subgraphs. In particular, this theorem combines several of the separate results of [4] and may cover some further examples as well. Our proof follows closely the direct methods of [4], and makes use of a powerful theorem of [3], the gauge-invariant uniqueness theorem.…”
Section: Introductionmentioning
confidence: 65%
“…In particular, this theorem combines several of the separate results of [4] and may cover some further examples as well. Our proof follows closely the direct methods of [4], and makes use of a powerful theorem of [3], the gauge-invariant uniqueness theorem. Proposition 3.7 gives equivalent conditions to those of Theorem 3.1 which may make the theorem easier to apply, and which give some idea of what the contracted graph will look like.…”
Section: Introductionmentioning
confidence: 65%
See 3 more Smart Citations