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Journal of the London Mathematical Society Advance Access originally published online on October 18, 2007
Journal of the London Mathematical Society 2007 76(2):479-497; doi:10.1112/jlms/jdm066
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© 2007 London Mathematical Society

Property A, partial translation structures, and uniform embeddings in groups

J. Brodzki, G.A. Niblo and N.J. Wright

School of Mathematics
University of Southampton
Highfield
Southampton SO17 1BJ
United Kingdom
j.brodzki@soton.ac.uk
wright@soton.ac.uk

We define the concept of a partial translation structure T on a metric space X and 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.

2000 Mathematics Subject Classification 46L85, 20F65, 54E35.

Received March 24, 2006; revised February 7, 2007; published online October 18, 2007.


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