Higman–Thompson‐like groups of higher rank graph C*‐algebras

Abstract

Let Λ be a row-finite and source-free higher rank graph with finitely many vertices. In this paper, we define the Higman-Thompson-like group Λ ht of the graph C*algebra  Λ to be a special subgroup of the unitary group in  Λ . It is shown that Λ ht is closely related to the topological full groups of the groupoid associated with Λ. Some properties of Λ ht are also investigated. We show that its commutator group Λ ′ ht is simple and that Λ ′ ht has only one non-trivial uniformly recurrent subgroup if Λ is aperiodic and strongly connected. Furthermore, if Λ is single-vertex, then we prove that Λ ht is C*-simple and also provide an explicit description on the stabilizer uniformly recurrent subgroup of Λ ht under a natural action on the infinite path space of Λ. M S C ( 2 0 2 0 ) 46L05 (primary), 20F99 (secondary)