C*-simplicity and representations of topological full groups of groupoids

TY - JOUR

T1 - C*-simplicity and representations of topological full groups of groupoids

AU - Brix, Kevin Aguyar

AU - Scarparo, Eduardo

PY - 2019/11/1

Y1 - 2019/11/1

N2 - Given an ample groupoid G with compact unit space, we study the canonical representation of the topological full group [[G]] in the full groupoid C⁎-algebra C⁎(G). In particular, we show that the image of this representation generates C⁎(G) if and only if C⁎(G) admits no tracial state. The techniques that we use include the notion of groups covering groupoids. As an application, we provide sufficient conditions for C⁎-simplicity of certain topological full groups, including those associated with topologically free and minimal actions of non-amenable and countable groups on the Cantor set.

AB - Given an ample groupoid G with compact unit space, we study the canonical representation of the topological full group [[G]] in the full groupoid C⁎-algebra C⁎(G). In particular, we show that the image of this representation generates C⁎(G) if and only if C⁎(G) admits no tracial state. The techniques that we use include the notion of groups covering groupoids. As an application, we provide sufficient conditions for C⁎-simplicity of certain topological full groups, including those associated with topologically free and minimal actions of non-amenable and countable groups on the Cantor set.

U2 - 10.1016/j.jfa.2019.06.014

DO - 10.1016/j.jfa.2019.06.014

M3 - Journal article

SN - 0022-1236

VL - 277

SP - 2981

EP - 2996

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 9

ER -