Higher dimensional generalizations of the Thompson groups via higher rank graphs

We show how to construct a family of groups from a family of monoids that generalize free monoids. In the case of free monoids on two or more finite generators, we get back the familiar Thompson groups. The family of monoids that arise should be of independent interest. The motivation for defining this family comes from the theory of C*-algebras. This is joint work with Alina Vdovina (CCNY) and Aidan Sims (Wollongong).