Property A, partial translation structures and uniform embeddings in groups

2006/03/27 by J. Brodzki, Brodzki, J., G. A. Niblo +3 · 1 citation
Mathematics · #58B34 #FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA) #math.GR #math.OA #msc:58B34

paper · pdf · doi:10.48550/arxiv.math/0603621

arxiv created 2007/02/20 · arxiv updated 2009/12/01

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.

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• Partial Translation Algebras for Trees

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