Uniform Roe Algebras as Crossed Product

  • 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 􀡳 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.

Published
2018-05-11
How to Cite
KANNAN, Kankeyanathan. Uniform Roe Algebras as Crossed Product. GSTF Journal of Mathematics, Statistics and Operations Research (JMSOR), [S.l.], v. 2, n. 1, may 2018. ISSN 2251-3396. Available at: <http://dl6.globalstf.org/index.php/jmsor/article/view/1511>. Date accessed: 19 dec. 2018.