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arXiv · math/0603621

Property A, partial translation structures and uniform embeddings in groups

J. Brodzki·G. A. Niblo·N. J. Wright
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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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J. Brodzki, G. A. Niblo, N. J. Wright. 2007-02-20. Property A, partial translation structures and uniform embeddings in groups. https://arxiv.org/abs/math/0603621

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