379 research outputs found
On the K-theory of twisted higher-rank-graph C*-algebras
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.Comment: 15 pages; four diagrams prepared in Tik
UCT-Kirchberg algebras have nuclear dimension one
We prove that every Kirchberg algebra in the UCT class has nuclear dimension
1. We first show that Kirchberg 2-graph algebras with trivial and finite
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.Comment: 21 pages. Version 2: reference [2] has been added, and the discussion
in the introduction updated; a small but important typo has been corrected in
the definition of the graph E_T. Version 3: Some typo's corrected and
references updated; reference [2] corrected as we had accidentally omitted
one of the authors' names in the previous version (sorry Aaron!); this
version to appear in Adv. Mat
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