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Full-Text Articles in Social and Behavioral Sciences
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 The C-Algebras Of Reducible Graphs, Astrid An Huef, Marcelo Laca, Iain Raeburn, Aidan Sims
Kms States On The C-Algebras Of Reducible Graphs, Astrid An Huef, Marcelo Laca, Iain Raeburn, Aidan Sims
Faculty of Engineering and Information Sciences - Papers: Part A
We consider the dynamics on the C-algebras of finite graphs obtained by lifting the gauge action to an action of the real line. Enomoto, Fujii and Watatani [KMS states for gauge action on OA. Math. Japon. 29 (1984), 607-619] proved that if the vertex matrix of the graph is irreducible, then the dynamics on the graph algebra admits a single Kubo-Martin-Schwinger (KMS) state. We have previously studied the dynamics on the Toeplitz algebra, and explicitly described a finite-dimensional simplex of KMS states for inverse temperatures above a critical value. Here we study the KMS states for graphs with reducible vertex …
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 …
Group Actions On Labeled Graphs And Their C*-Algebras, Teresa Bates, David Pask, Paulette Willis
Group Actions On Labeled Graphs And Their C*-Algebras, Teresa Bates, David Pask, Paulette Willis
Faculty of Engineering and Information Sciences - Papers: Part A
We introduce the notion of the action of a group on a labeled graph and the quotient object, also a labeled graph. We define a skew product labeled graph and use it to prove a version of the Gross–Tucker theorem for labeled graphs. We then apply these results to the C -algebra associated to a labeled graph and provide some applications in non-Abelian duality.
Zappa-Szep Products Of Semigroups And Their C*-Algebras, Nathan D. Brownlowe, Jacqueline Ramagge, David I. Robertson, Michael F. Whittaker
Zappa-Szep Products Of Semigroups And Their C*-Algebras, Nathan D. Brownlowe, Jacqueline Ramagge, David I. Robertson, Michael F. Whittaker
Faculty of Engineering and Information Sciences - Papers: Part A
Zappa-Szep products of semigroups provide a rich class of examples of semigroups that include the self-similar group actions of Nekrashevych. We use Li's construction of semigroups C*-algebras to associate a C*-algebra to Zappa-Szep products and give an explicit presentation of the algebra. We then define a quotient C*-algebra that generalises the Cuntz-Pimsner algebras for self-similar actions. We indicate how knowne examples, previously viewed as distinct classes, fit into our unifying framework. We specifically discuss the Baumslag-Solitar groups, the binary adding machine, the semigroup NXNx, and the ax+b semigroup ZXZx.
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.
Equilibrium States On The Cuntz-Pimsner Algebras Of Self-Similar Actions, Marcelo Laca, Iain Raeburn, Jacqui Ramagge, Michael Whittaker
Equilibrium States On The Cuntz-Pimsner Algebras Of Self-Similar Actions, Marcelo Laca, Iain Raeburn, Jacqui Ramagge, Michael Whittaker
Faculty of Engineering and Information Sciences - Papers: Part A
We consider a family of Cuntz-Pimsner algebras associated to self-similar group actions, and their Toeplitz analogues. Both families carry natural dynamics implemented by automorphic actions of the real line, and we investigate the equilibrium states (the KMS states) for these dynamical systems. We find that for all inverse temperatures above a critical value, the KMS states on the Toeplitz algebra are given, in a very concrete way, by traces on the full group algebra of the group. At the critical inverse temperature, the KMS states factor through states of the Cuntz-Pimsner algebra; if the self-similar group is contracting, then the …
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 …
Omitting Types And Af Algebras, Kevin Carlson, Enoch Cheung, Ilijas Farah, Alexander Gerhardt-Bourke, Bradd Hart, Leanne Mezuman, Nigel Sequeira, Alexander Sherman
Omitting Types And Af Algebras, Kevin Carlson, Enoch Cheung, Ilijas Farah, Alexander Gerhardt-Bourke, Bradd Hart, Leanne Mezuman, Nigel Sequeira, Alexander Sherman
Faculty of Engineering and Information Sciences - Papers: Part A
We prove that the classes of UHF algebras and AF algebras, while not axiomatizable, can be characterized as those C*-algebras that omit certain types in the logic of metric structures.