Uniform Roe Algebras as Crossed Product
We define what a coarse space is, and we study a number of ways of constructing a coarse structure on a set so as to make it into a coarse space. We also consider some of the elementary concepts associated with coarse spaces. A discrete group has natural coarse structure which allows us to define the uniform Roe algebra, . The reduced algebra is naturally contained in . In this paper, we will characterize as a crossed product.