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Full-Text Articles in Social and Behavioral Sciences
On The K-Theory Of Twisted Higher-Rank-Graph C*-Algebras, Alex Kumjian, David Pask, Aidan Sims
On The K-Theory Of Twisted Higher-Rank-Graph C*-Algebras, Alex Kumjian, David Pask, Aidan Sims
Faculty of Engineering and Information Sciences - Papers: Part A
We investigate the K-theory of twisted higher-rank-graph algebras by adapting parts of Elliott's computation of the K-theory of the rotation algebras. We show that each 2-cocycle on a higher-rank graph taking values in an abelian group determines a continuous bundle of twisted higher-rank graph algebras over the dual group. We use this to show that for a circle-valued 2-cocycle on a higher-rank graph obtained by exponentiating a real-valued cocycle, the K-theory of the twisted higher-rank graph algebra coincides with that of the untwisted one.
Kms States On The C*-Algebras Of Finite Graphs, Astrid An Huef, Marcelo Laca, Iain F. Raeburn, Aidan D. Sims
Kms States On The C*-Algebras Of Finite Graphs, Astrid An Huef, Marcelo Laca, Iain F. Raeburn, Aidan D. Sims
Faculty of Engineering and Information Sciences - Papers: Part A
We consider a finite directed graph E, and the gauge action on its Toeplitz-Cuntz-Krieger algebra, viewed as an action of R. For inverse temperatures larger than a critical value βc, we give an explicit construction of all the KMSβ states. If the graph is strongly connected, then there is a unique KMSβc state, and this state factors through the quotient map onto C*(E). Our approach is direct and relatively elementary.
Remarks On Some Fundamental Results About Higher-Rank Graphs And Their C*-Algebras, Robert Hazlewood, Iain Raeburn, Aidan Sims, Samuel B. G Webster
Remarks On Some Fundamental Results About Higher-Rank Graphs And Their C*-Algebras, Robert Hazlewood, Iain Raeburn, Aidan Sims, Samuel B. G Webster
Faculty of Engineering and Information Sciences - Papers: Part A
Results of Fowler and Sims show that every k-graph is completely determined by its k-coloured skeleton and collection of commuting squares. Here we give an explicit description of the k-graph associated with a given skeleton and collection of squares and show that two k-graphs are isomorphic if and only if there is an isomorphism of their skeletons which preserves commuting squares. We use this to prove directly that each k-graph. is isomorphic to the quotient of the path category of its skeleton by the equivalence relation determined by the commuting squares, and show that this extends to a homeomorphism of …