Property A, partial translation structures and uniform embeddings in groups

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

2006-03-27

arxiv.org/abs/math/0603621v2

Mathematics

Operator Algebras

Scientific paper

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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