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One-Parameter Continuous Fields of Kirchberg Algebras

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Abstract

We prove that all unital separable continuous fields of C*-algebras over [0,1] with fibers isomorphic to the Cuntz algebra \({\mathcal{O}}_n \, (2 \leq n \leq \infty)\) are trivial. More generally, we show that if A is a separable, unital or stable, continuous field over [0,1] of Kirchberg C*-algebras satisfying the UCT and having finitely generated K-theory groups, then A is isomorphic to a trivial field if and only if the associated K-theory presheaf is trivial. For fixed \(d\in \{0,1\}\) we also show that, under the additional assumption that the fibers have torsion free K d -group and trivial K d+1-group, the K d -sheaf is a complete invariant for separable stable continuous fields of Kirchberg algebras.

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Authors and Affiliations

  1. Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA

    Marius Dadarlat

  2. Department of Mathematics, University of Toronto, Toronto, Ontario, Canada, M5S 3G3

    George A. Elliott

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  1. Marius Dadarlat
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  2. George A. Elliott
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Correspondence to Marius Dadarlat.

Additional information

Communicated by Y. Kawahigashi

M.D. was supported in part by NSF Grant #DMS-0500693.

G.A.E. held a Discovery Grant from NSERC Canada.

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Dadarlat, M., Elliott, G.A. One-Parameter Continuous Fields of Kirchberg Algebras. Commun. Math. Phys. 274, 795–819 (2007). https://doi.org/10.1007/s00220-007-0298-z

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