C*-simplicity and representations of topological full groups of groupoids
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C*-simplicity and representations of topological full groups of groupoids. / Brix, Kevin Aguyar; Scarparo, Eduardo.
I: Journal of Functional Analysis, Bind 277, Nr. 9, 2019, s. 2981-2996.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - C*-simplicity and representations of topological full groups of groupoids
AU - Brix, Kevin Aguyar
AU - Scarparo, Eduardo
PY - 2019
Y1 - 2019
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
VL - 277
SP - 2981
EP - 2996
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 9
ER -
ID: 222871316