Uniform Roe Algebras as Crossed Product

DOI: 10.5176/2251-3388_2.1.23

Authors: Kankeyanathan Kannan

Abstract:

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 G has natural coarse structure which allows us to define the uniform Roe algebra, C*u(G). The reduced C* - algebra C*r(G) is naturally contained in C*u(G). In this paper, we will characterize C*u(G) as a crossed product.

Keywords: Invariant Approximation Property, Uniform Roe algebras