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Articles 1 - 13 of 13
Full-Text Articles in Social and Behavioral Sciences
Topological Spaces Associated To Higher-Rank Graphs, Alexander Kumjian, David Pask, Aidan Sims, Michael F. Whittaker
Topological Spaces Associated To Higher-Rank Graphs, Alexander Kumjian, David Pask, Aidan Sims, Michael F. Whittaker
Faculty of Engineering and Information Sciences - Papers: Part A
We investigate which topological spaces can be constructed as topological realisations of higher-rank graphs. We describe equivalence relations on higher-rank graphs for which the quotient is again a higher-rank graph, and show that identifying isomorphic co-hereditary subgraphs in a disjoint union of two rank-k graphs gives rise to pullbacks of the associated C*-algebras. We describe a combinatorial version of the connected-sum operation and apply it to the rank-2-graph realisations of the four basic surfaces to deduce that every compact 2-manifold is the topological realisation of a rank-2 graph. We also show how to construct k-spheres and wedges of k-spheres as …
Twisted K-Graph Algebras Associated To Bratteli Diagrams, David Pask, Adam Sierakowski, Aidan Sims
Twisted K-Graph Algebras Associated To Bratteli Diagrams, David Pask, Adam Sierakowski, Aidan Sims
Faculty of Engineering and Information Sciences - Papers: Part A
2015 Springer Basel Given a system of coverings of k-graphs, we show that the second cohomology of the resulting (k + 1)-graph is isomorphic to that of any one of the k-graphs in the system, and compute the semifinite traces of the resulting twisted (k + 1)-graph C*-algebras. We then consider Bratteli diagrams of 2-graphs whose twisted C*-algebras are matrix algebras over noncommutative tori. For such systems we calculate the ordered K-theory of the resulting twisted 3-graph C*-algebras. We deduce that every such C*-algebra is Morita equivalent to the C*-algebra of a rank-2 Bratteli diagram in the sense of Pask-Raeburn-Rørdam-Sims.
Purely Infinite C*-Algebras Associated To Etale Groupoids, Jonathon Brown, Les Clark, Adam Sierakowski
Purely Infinite C*-Algebras Associated To Etale Groupoids, Jonathon Brown, Les Clark, Adam Sierakowski
Faculty of Engineering and Information Sciences - Papers: Part A
No abstract provided.
Kms States On C*-Algebras Associated To Higher-Rank Graphs, Astrid An Huef, Marcelo Laca, Iain Raeburn, Aidan Sims
Kms States On C*-Algebras Associated To Higher-Rank Graphs, Astrid An Huef, Marcelo Laca, Iain Raeburn, Aidan Sims
Faculty of Engineering and Information Sciences - Papers: Part A
Consider a higher rank graph of rank k. Both the Cuntz-Krieger algebra and Toeplitz-Cuntz-Krieger algebra of the graph carry natural gauge actions of the torus Tk, and restricting these guage actions to one parameter subgroups of Tk gives dynamical systems involving actions of the real line. We study the KMS states of these dynamical systems. We find that for large inverse temperatures B, the simplex of KMS B states of the Toeplitz-Cuntz-Krieger algebra has dimension d one less than the number of vertices in the graph. We also show that there is a preferred dynamics for which there is a …
Simplicity Of Algebras Associated To Étale Groupoids, Jonathan Brown, Lisa Orloff Clark, Cynthia Farthing, Aidan Sims
Simplicity Of Algebras Associated To Étale Groupoids, Jonathan Brown, Lisa Orloff Clark, Cynthia Farthing, Aidan Sims
Faculty of Engineering and Information Sciences - Papers: Part A
We prove that the full C*-algebra of a second-countable, Hausdorff, etale, amenable groupoid is simple if and only if the groupoid is both topologically principal and minimal. We also show that if G has totally disconnected unit space, then the complex *-algebra of its inverse semigroup of compact open bisections, as introduced by Steinberg, is simple if and only if G is both effective and minimal.
Twisted C-Algebras Associated To Finitely Aligned Higher-Rank Graphs, Aidan Sims, Benjamin Whitehead, Michael Whittaker
Twisted C-Algebras Associated To Finitely Aligned Higher-Rank Graphs, Aidan Sims, Benjamin Whitehead, Michael Whittaker
Faculty of Engineering and Information Sciences - Papers: Part A
We introduce twisted relative Cuntz-Krieger algebras associated to finitely aligned higher-rank graphs and give a comprehensive treatment of their fundamental structural properties. We establish versions of the usual uniqueness theorems and the classification of gauge-invariant ideals. We show that all twisted relative Cuntz- Krieger algebras associated to finitely aligned higher-rank graphs are nuclear and satisfy the UCT, and that for twists that lift to real-valued cocycles, the K-theory of a twisted relative Cuntz-Krieger algebra is independent of the twist. In the final section, we identify a sufficient condition for simplicity of twisted Cuntz-Krieger algebras associated to higher-rank graphs which are …
An Elementary Approach To C*-Algebras Associated To Topological Graphs, Hui Li, David Pask, Aidan Sims
An Elementary Approach To C*-Algebras Associated To Topological Graphs, Hui Li, David Pask, Aidan Sims
Faculty of Engineering and Information Sciences - Papers: Part A
We develop notions of a representation of a toopological grapph E and of a covariant representation of a topological graph E which do onot require the machinery of C* -correspondences and Cuntz-Pimsner alegebars. We show that the C* -algebra generated by a universal representation of E is isomorphic to the Toeplitz algebra of Katsura's topological-graph bimodule, and that the C* palgebra generated by a universal covariant representation of E is isomorphic to Katsura's topological graph C* -algebra. We exhibit our resluts by constructing the isomorphism between the C* -algebra of the row-finite directed graph E with no sources and the …
Purely Infinite Simple C*-Algebras Associated To Integer Dilation Matrices, Ruy Exel, Astrid An Huef, Iain Raeburn
Purely Infinite Simple C*-Algebras Associated To Integer Dilation Matrices, Ruy Exel, Astrid An Huef, Iain Raeburn
Faculty of Engineering and Information Sciences - Papers: Part A
Given an n×n integer matrix A whose eigenvalues are strictly greater than 1 in absolute value, let σA be the transformation of the n-torus Tn = Rn/Zn defined by σA(e2πix) = e2πiAx for x ∈ Rn. We study the associated crossed-product C∗-algebra, which is defined using a certain transfer operator for σA, proving it to be simple and purely infinite and computing its K-theory groups.
C*-Algebras Associated To C*-Correspondences And Applications To Mirror Quantum Spheres, David I. Robertson, Wojciech Szymanski
C*-Algebras Associated To C*-Correspondences And Applications To Mirror Quantum Spheres, David I. Robertson, Wojciech Szymanski
Faculty of Engineering and Information Sciences - Papers: Part A
The structure of the C*-algebras corresponding to even-dimensional mirror quantum spheres is investigated. It is shown that they are isomorphic to both Cuntz-Pimsner algebras of certain C*-correspondences and C*-algebras of certain labelled graphs. In order to achieve this, categories of labelled graphs and C*-correspondences are studied. A functor from labelled graphs to C*-correspondences is constructed, such that the corresponding associated C*-algebras are isomorphic. Furthermore, it is shown that C*-correspondences for the mirror quantum spheres arise via a general construction of restricted direct sum.
Semifinite Spectral Triples Associated With Graph C*-Algebras, Alan L. Carey, John Phillips, Adam Rennie
Semifinite Spectral Triples Associated With Graph C*-Algebras, Alan L. Carey, John Phillips, Adam Rennie
Faculty of Engineering and Information Sciences - Papers: Part A
We review the recent construction of semifinite spectral triples for graph C^*-algebras. These examples have inspired many other developments and we review some of these such as the relation between the semifinite index and the Kasparov product, examples of noncommutative manifolds, and an index theorem in twisted cyclic theory using a KMS state.
Actions Of Z^K Associated To Higher Rank Graphs, Alexander Kumjian, David Pask
Actions Of Z^K Associated To Higher Rank Graphs, Alexander Kumjian, David Pask
Faculty of Engineering and Information Sciences - Papers: Part A
An action of Zk is associated to a higher rank graph Λ satisfying a mild assumption. This generalizes the construction of a topological Markov shift arising from a non-negative integer matrix. We show that the stable Ruelle algebra of Λ is strongly Morita equivalent to C∗(Λ). Hence, if Λ satisfies the aperiodicity condition, the stable Ruelle algebra is simple, stable and purely infinite.
Slope Instability, Hazard And Risk Associated With A Rainstorm Event - A Case Study, Phillip N. Flentje, Robin N. Chowdhury
Slope Instability, Hazard And Risk Associated With A Rainstorm Event - A Case Study, Phillip N. Flentje, Robin N. Chowdhury
Faculty of Engineering and Information Sciences - Papers: Part A
Over the last few decades there has been an increasing awareness of landslide hazard and risk in many coastal regions of Australia. Urban communities in hilly areas are, from time to time, adversely affected by rainfall-induced landsliding. However, acute awareness of hazard may be absent during periods between significant rainstorm events. In general, the serious consequences of landslides to property and life have been underestimated in Australia. It is now known that at least 80 deaths can be attributed to a number of landslides (Leiba, 1998). Some of these events have focussed the attention of the public, the most important …
Molecular Epidemiology Of A Fast-Food Restaurant-Associated Outbreak Of Escherichia Coli O157:H7 In Washington State, Linda M. Grimm, Marcia Goldoft, John Kobayashi, Jay H. Lewis, Dalia Alfi, Ann Marie Perdichizzi, Phillip I. Tarr, Jerry E. Ongerth, Steve L. Moseley, Mansour Samadpour
Molecular Epidemiology Of A Fast-Food Restaurant-Associated Outbreak Of Escherichia Coli O157:H7 In Washington State, Linda M. Grimm, Marcia Goldoft, John Kobayashi, Jay H. Lewis, Dalia Alfi, Ann Marie Perdichizzi, Phillip I. Tarr, Jerry E. Ongerth, Steve L. Moseley, Mansour Samadpour
Faculty of Engineering and Information Sciences - Papers: Part A
We studied the molecular epidemiology of the recent fast-food restaurant chain-associated Escherichia coli O157:H7 outbreak in Washington State. Genomic DNAs prepared from strains isolated from 433 patients were probed with radiolabelled Shiga-like toxin (SLT) I and SLT II genes and bacteriophage l DNA and were subsequently analyzed for their restriction fragment length polymorphism (RFLP) patterns. The SLT RFLP and l RFLP profiles of an E. coli O157:H7 strain isolated from the incriminated beef and prototype patient were compared with those of the patient isolates for determination of the concordance between patterns. Of the 377 patients with primary and secondary cases …