A Deaconu–Renault system consists of a partially defined local homeomorphism on a locally compact Hausdorff space, and for each such system there is an associated amenable Hausdorff étale groupoid. Deaconu–Renault systems give rise to a large class of (groupoid) C-algebras that, in particular, includes graph C-algebras,
crossed products by actions of the integers, and all Kirchberg algebras satisfying the UCT. In this talk I will introduce a notion of (topological) conjugacy of Deaconu–Renault systems, and I will show how to recover the conjugacy class of a Deaconu–Renault system from its associated groupoid or groupoid C*-algebra. (This is joint work with Kevin Aguyar Brix, Toke Meier Carlsen, and Søren Eilers.)
This video was produced by the International Centre for Mathematical Sciences, as part of the workshop Algebra, Geometry and C*-algebras.