TY - JOUR
AU - Borys, Clemens
PY - 2021/08/31
Y2 - 2021/09/19
TI - A groupoid picture of the Elek algebras
JF - MATHEMATICA SCANDINAVICA
JA - Math. Scand.
VL - 127
IS - 2
SE - Articles
DO - 10.7146/math.scand.a-122419
UR - https://www.mscand.dk/article/view/122419
SP - 185-208
AB - <p>We reformulate a construction by GĂˇbor Elek, which associates $C^{\ast} $-algebras with uniformly recurrent subgroups, in the language of groupoid $C^{\ast} $-algebras. This allows us to simplify several proofs from the original paper and add the converse direction to Elek's characterisation of nuclearity, showing that his sufficient condition is in fact necessary. We furthermore relate our groupoids to the dynamics of the group acting on its uniformly recurrent subgroup.</p>
ER -