A Class of C*-Algebras Generalizing Both Graph Algebras and Homeomorphism C*-Algebras Ii, Examples

Katsura, Takeshi

doi:10.1142/s0129167x06003722

Cited by 93 publications

(258 citation statements)

References 27 publications

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“…Applying a result of Katsura ([11, Corollary 6.10]) we get the following (in the notation of [11], E{oof rg = E{oof since ^(^(^(oo) 1 ) = E(oo)° and £(oo)° is compact).…”

Section: If • G)(y) = F(mentioning

confidence: 91%

“…Recall that a topological graph is given by a quadruple F = (F°, F l , s F , r F ) [13] Limit algebras and directed graphs 357 map. To a topological graph F one associates a graph C*-algebra, written O(F) ( [11] and [20]). We will not go into the details of the definition of O(F), but just note that it generalizes O(F) for finite graphs and it is the Cuntz-Pimsner C*-algebra associated with a C*-correspondence constructed from the graph.…”

Section: ) •mentioning

confidence: 99%

“…Since Ki(C(E(n k ) 0 )) = {0} for each k, the second statement of the lemma also follows. D Given the topological graph £(oo), one can associate with it a C*-correspondence Z over A = C(Y) as follows (see also [11,18,20]). On the space C(£(oo)') one can define a (right) C(K)-module structure by setting To make this module into a correspondence one defines, for / 6 C{Y), is € C(£(oo)'), (f\jf){e, w) = f(a e (w))ijr (e, w).…”

Section: K -Theorymentioning

confidence: 99%

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A Class of Limit Algebras Associated with Directed Graphs

Kribs¹,

Solel²

2007

J. Aust. Math. Soc.

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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.

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“…Applying a result of Katsura ([11, Corollary 6.10]) we get the following (in the notation of [11], E{oof rg = E{oof since ^(^(^(oo) 1 ) = E(oo)° and £(oo)° is compact).…”

Section: If • G)(y) = F(mentioning

confidence: 91%

Section: ) •mentioning

confidence: 99%

Section: K -Theorymentioning

confidence: 99%

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A Class of Limit Algebras Associated with Directed Graphs

Kribs¹,

Solel²

2007

J. Aust. Math. Soc.

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“…Over the last ten years, graph C * -algebras and their analogues have been the subject of intense research interest (see for example [5,7,8,13,16,20,25,38], or see [30] for a good overview). In particular, the higher-rank graphs and associated C * -algebras introduced in [18] have recently been widely studied [10,12,19,28].…”

Section: Introductionmentioning

confidence: 99%

Generalised morphisms of 𝑘-graphs: 𝑘-morphs

Kumjian

Pask

Sims

2010

Trans. Amer. Math. Soc.

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Abstract. In a number of recent papers, (k+l)-graphs have been constructed from k-graphs by inserting new edges in the last l dimensions. These constructions have been motivated by C * -algebraic considerations, so they have not been treated systematically at the level of higher-rank graphs themselves. Here we introduce k-morphs, which provide a systematic unifying framework for these various constructions. We think of k-morphs as the analogue, at the level of k-graphs, of C * -correspondences between C * -algebras. To make this analogy explicit, we introduce a category whose objects are k-graphs and whose morphisms are isomorphism classes of k-morphs. We show how to extend the assignment Λ → C * (Λ) to a functor from this category to the category whose objects are C * -algebras and whose morphisms are isomorphism classes of C * -correspondences.

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“…In the best case they may be completely classified by the theorem of Kirchberg [17] and Phillips [20]: generalized Cuntz-Krieger algebras are often purely infinite and thus determine candidates in advance. The computation of the K -theory of rank-one graph C * -algebras, see [11,16,19,25,30], and Cuntz-Krieger and Exel-Laca algebras, see [9,10,14], is completed.…”

Section: Introductionmentioning

confidence: 99%