Higher Rank Graph C-Algebras
By Alex Kumjian, David Pask. 2000
154 citations recorded by the source corpus.
Building on recent work of Robertson and Steger, we associate a C{algebra to a combinatorial object which may be thought of as a higher rank graph. This C{algebra is shown to be isomorphic to that of the associ- ated path groupoid. Various results in this paper give sucient conditions on the higher rank graph for the associated C{algebra to be: simple, purely in- nite and AF. Results concerning the structure of crossed products by certain natural actions of discrete groups are obtained; a technique for constructing rank 2 graphs from \commuting" rank 1 graphs is given.
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/4fa1fa111c05089e45b58e467997449d53896f25
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In Algebra and Number Theory
In Mathematical Physics
Citations in the corpus
- The Noncommutative Geometry of k-graph C*-Algebras (2005, methodology): “The factorisation property ensures (see [ KP ]) that the identity morphisms of � are precisely the morphisms of degree 0; that is {ido : o ∈ Obj(�)} = d −1 (0).”
- Product systems of graphs and the Toeplitz algebras of higher-rank graphs | NOVA. The University of Newcastle's Digital Repository (2003, methodology): “If � is a row-finite k-graph with no sources, it follows from Lemma 6.1 that C�(E�) is the C�-algebra C�(�) studied in [ 11 ].”
- Product systems over right-angled Artin semigroups (2001, methodology): “When S is a monoid with no nontrivial idempotents, product systems over S that take values in this category are related to the k-graphs of Kumjian-Pask [ 12 ].”
- C*-algebras associated to product systems of hilbert bimodules (2007, background): “Kumjian and Pask’s uniqueness theorems for higher-rank graph C ∗-algebras [ 19 ] suggest that Fowler’s notion of Cuntz-Pimsner covariance determines a universal C ∗-algebra which satisfies (A) and (B) of Section 1.2 when (G,P) = (Zk, Nk), and each �p is injective with �p(A) ⊂ K(Xp).”