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Full-Text Articles in Social and Behavioral Sciences
The Nuclear Dimension Of Graph C*-Algebras, Efren Ruiz, Aidan Sims, Mark Tomforde
The Nuclear Dimension Of Graph C*-Algebras, Efren Ruiz, Aidan Sims, Mark Tomforde
Faculty of Engineering and Information Sciences - Papers: Part A
Consider a graph C⁎C⁎-algebra C⁎(E)C⁎(E) with a purely infinite ideal I (possibly all of C⁎(E)C⁎(E)) such that I has only finitely many ideals and C⁎(E)/IC⁎(E)/I is approximately finite dimensional. We prove that the nuclear dimension of C⁎(E)C⁎(E) is 1. If I has infinitely many ideals, then the nuclear dimension of C⁎(E)C⁎(E) is either 1 or 2.
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.
Von Neumann Algebras Of Strongly Connected Higher-Rank Graphs, Marcelo Laca, Nadia S. Larsen, Sergey Neshveyev, Aidan Sims, Samuel B. Webster
Von Neumann Algebras Of Strongly Connected Higher-Rank Graphs, Marcelo Laca, Nadia S. Larsen, Sergey Neshveyev, Aidan Sims, Samuel B. Webster
Faculty of Engineering and Information Sciences - Papers: Part A
We investigate the factor types of the extremal KMS states for the preferred dynamics on the Toeplitz algebra and the Cuntz-Krieger algebra of a strongly connected finite (Formula presented.)-graph. For inverse temperatures above 1, all of the extremal KMS states are of type (Formula presented.). At inverse temperature 1, there is a dichotomy: if the (Formula presented.)-graph is a simple (Formula presented.)-dimensional cycle, we obtain a finite type (Formula presented.) factor; otherwise we obtain a type III factor, whose Connes invariant we compute in terms of the spectral radii of the coordinate matrices and the degrees of cycles in the …
Uct-Kirchberg Algebras Have Nuclear Dimension One, Efren Ruiz, Aidan Sims, Adam P. Sorensen
Uct-Kirchberg Algebras Have Nuclear Dimension One, Efren Ruiz, Aidan Sims, Adam P. Sorensen
Faculty of Engineering and Information Sciences - Papers: Part A
We prove that every Kirchberg algebra in the UCT class has nuclear dimension 1. We first show that Kirchberg 2-graph algebras with trivial K0 and finite K1 have nuclear dimension 1 by adapting a technique developed by Winter and Zacharias for Cuntz algebras. We then prove that every Kirchberg algebra in the UCT class is a direct limit of 2-graph algebras to obtain our main theorem.