Topological full groups of ample groupoids with applications to graph algebras
Journal article, Peer reviewed
Published version
Åpne
Permanent lenke
http://hdl.handle.net/11250/2595588Utgivelsesdato
2019Metadata
Vis full innførselSamlinger
- Institutt for matematiske fag [2474]
- Publikasjoner fra CRIStin - NTNU [38289]
Originalversjon
10.1142/S0129167X19500186Sammendrag
We study the topological full group of ample groupoids over locally compact spaces. We extend Matui’s definition of the topological full group from the compact to the locally compact case. We provide two general classes of étale groupoids for which the topological full group, as an abstract group, is a complete isomorphism invariant, hereby extending Matui’s Isomorphism Theorem. As an application, we study graph groupoids and their topological full groups, and obtain sharper results for this class. The machinery developed in this process is used to prove an embedding theorem for ample groupoids, akin to Kirchberg’s Embedding Theorem for C∗-algebras. Consequences for graph C∗-algebras and Leavitt path algebras are also spelled out. In particular, we improve on a recent embedding theorem of Brownlowe and Sørensen for Leavitt path algebras.