The nuclear dimension of C*-algebras

Winter, W. and Zacharias, J. (2010) The nuclear dimension of C*-algebras. Advances in Mathematics, 224(2), pp. 461-498. (doi:10.1016/j.aim.2009.12.005)

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Publisher's URL: http://dx.doi.org/10.1016/j.aim.2009.12.005

Abstract

We introduce the nuclear dimension of a C*-algebra; this is a noncommutative version of topological covering dimension based on a modification of the earlier concept of decomposition rank. Our notion behaves well with respect to inductive limits, tensor products, hereditary subalgebras (hence ideals), quotients, and even extensions. It can be computed for many examples; in particular, it is finite for all UCT Kirchberg algebras. In fact, all classes of nuclear C*-algebras which have so far been successfully classified consist of examples with finite nuclear dimension, and it turns out that finite nuclear dimension implies many properties relevant for the classification program. Surprisingly, the concept is also linked to coarse geometry, since for a discrete metric space of bounded geometry the nuclear dimension of the associated uniform Roe algebra is dominated by the asymptotic dimension of the underlying space.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Zacharias, Dr Joachim
Authors: Winter, W., and Zacharias, J.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Advances in Mathematics
Journal Abbr.:Adv. Math.
ISSN:0001-8708
ISSN (Online):1090-2082

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