Graph Algebras

Raeburn, Iain

doi:10.1090/cbms/103

Cited by 326 publications

(414 citation statements)

References 0 publications

Supporting

Mentioning

411

Contrasting

Order By: Relevance

“…We recall some terminology for graphs (see, for example, [12,2]; note that our edge direction convention agrees with that used in these papers and in [11], which is opposite to that used in [14]). …”

Section: Paths and Condition (K)mentioning

confidence: 99%

“…, n k } and l(α) = k. Then one can verify that β z (t α ) = z l(α) t α . It follows (see, for example, the argument of [14,Corollary 3.3]) that the fixed point algebra C * (E) β of the action β satisfies…”

Section: Gauge-invariant Idealsmentioning

confidence: 99%

“…This theory has been explored extensively in many papers (see [12,13,2,8] for seminal results, and [14] for a survey). Graph C * -algebras include many C * -algebras besides the Cuntz-Krieger algebras; in particular, graph C * -algebras include the Toeplitz algebra, continuous functions on the circle, all finite-dimensional C * -algebras, many AF-algebras, many purely infinite simple C * -algebras, and many Type I C * -algebras.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Graph algebras, Exel-Laca algebras, and ultragraph algebras coincide up to Morita equivalence

Katsura¹,

Muhly²,

Sims³

et al. 2010

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

View full text Add to dashboard Cite

Abstract. We prove that the classes of graph algebras, Exel-Laca algebras, and ultragraph algebras coincide up to Morita equivalence. This result answers the long-standing open question of whether every Exel-Laca algebra is Morita equivalent to a graph algebra. Given an ultragraph G we construct a directed graph E such that C * (G) is isomorphic to a full corner of C * (E). As applications, we characterize real rank zero for ultragraph algebras and describe quotients of ultragraph algebras by gauge-invariant ideals.

show abstract

Section: Paths and Condition (K)mentioning

confidence: 99%

Section: Gauge-invariant Idealsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Graph algebras, Exel-Laca algebras, and ultragraph algebras coincide up to Morita equivalence

Katsura¹,

Muhly²,

Sims³

et al. 2010

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

View full text Add to dashboard Cite

show abstract

“…For a recent survey of these algebras we point the reader to the notes [25]. Both O(E) and T(E) can be described either as universal objects or concretely.…”

Section: Or O(e)) and Its Toeplitz Extension T(e)mentioning

confidence: 99%

“…Our investigations draw on numerous aspects of contemporary operator algebra theory. We make use of fundamental results from the theory of graph C*-algebras [25] and Cuntz-Pimsner algebras [9,12,17,20,23]. The theory of C*-algebras associated with 'topological graphs', introduced by the second author and Muhly [19] and studied further in [11,12,13,20], plays a central role.…”

Section: Introductionmentioning

confidence: 99%

A Class of Limit Algebras Associated with Directed Graphs

Kribs¹,

Solel²

2007

J. Aust. Math. Soc.

View full text Add to dashboard Cite

Every directed graph defines a Hilbert space and a family of weighted shifts that act on the space. We identify a natural notion of periodicity for such shifts and study their C -algebras. We prove the algebras generated by all shifts of a fixed period are of Cuntz-Krieger and Toeplitz-Cuntz-Krieger type. The limit C*-algebras determined by an increasing sequence of positive integers, each dividing the next, are proved to be isomorphic to Cuntz-Pimsner algebras and the linking maps are shown to arise as factor maps. We derive a characterization of simplicity and compute the tf-groups for these algebras. We prove a classification theorem for the class of algebras generated by simple loop graphs.2000 Mathematics subject classification: primary 46L05,47L40.

show abstract

On Semicircular Elements Induced by Connected Finite Graphs

Cho

Jørgensen

2023

Mathematics Online First Collections

View full text Add to dashboard Cite

Graph Algebras

Cited by 326 publications

References 0 publications

Graph algebras, Exel-Laca algebras, and ultragraph algebras coincide up to Morita equivalence

Graph algebras, Exel-Laca algebras, and ultragraph algebras coincide up to Morita equivalence

A Class of Limit Algebras Associated with Directed Graphs

On Semicircular Elements Induced by Connected Finite Graphs

Contact Info

Product

Resources

About