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Property A, partial translation structures and uniform embeddings in groups

By Jacek Brodzki, Graham A. Niblo and Nick Wright

Abstract

We define the concept of a partial translation structure T on a metric space X and we show that there is a natural C*-algebra C*(T) associated with it which is a subalgebra of the uniform Roe algebra C*u(X). We introduce a coarse invariant of the metric which provides an obstruction to embedding the space in a group. When the space is sufficiently group-like, as determined by our invariant, properties of the Roe algebra can be deduced from those of C*(T). We also give a proof of the fact that the uniform Roe algebra of a metric space is a coarse invariant up to Morita equivalence

Topics: QA
Year: 2007
OAI identifier: oai:eprints.soton.ac.uk:44249
Provided by: e-Prints Soton

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