Property A, partial translation structures and uniform embeddings in groups
算子代数
2007-05-23 v2 群论
摘要
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.
引用
@article{arxiv.math/0603621,
title = {Property A, partial translation structures and uniform embeddings in groups},
author = {J. Brodzki and G. A. Niblo and N. J. Wright},
journal= {arXiv preprint arXiv:math/0603621},
year = {2007}
}