Property A, partial translation structures, and uniform embeddings in groups
By Jacek Brodzki, Graham A. Niblo, N. Wright. Journal of the London Mathematical Society, 2006
55 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/1fcd5cae5eca67e8c9e100ff14537ed610ef8283
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
In Geometry and Topology
- Rufus Willett
- Ján Špakula
- Goulnara Arzhantseva
- E. Guentner
- Martin Finn-Sell
- Guoliang Yu
- Denis V. Osin
- Nathanial P. Brown Narutaka Ozawa
In Mathematical Physics
- Rufus Willett
- Ján Špakula
- E. Guentner
- Goulnara Arzhantseva
- Martin Finn-Sell
- Guoliang Yu
- Nathanial P. Brown Narutaka Ozawa
- Damian Osajda
Citations in the corpus
- Maximal and reduced Roe algebras of coarsely embeddable spaces (2011, background): “The reader can easily check that the proof of Proposition 1.3 goes through for a general bounded geometry coarse space; however, the hypotheses for our main result Theorem 1.4 force a oarse space satisfying them to be metrisable.”
- Coarse Non-Amenability and Coarse Embeddings (2011, background): “The criterion from [1] does not readily apply.”