On nuclearity of the C∗-algebra of an inverse semigroup

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Massoud Amini
Tarbiat Modares University (Tehran, Iran). Department of Mathematics
Mahmood Khoshkam
University of Saskatchewan (Saskatoon, Canadà). Department of Mathematics and Statistics

We show that the universal groupoid of an inverse semigroup S is topologically (measurewise) amenable if and only if S is hyperfinite and all members of a family of subsemigroups of S indexed by the spectrum of the commutative C∗-algebra C∗(ES) on the idempotents ES of S are amenable. Thereby we solve some problems raised by A. L. T. Paterson.

Paraules clau
inverse semigroup, universal groupoid, amenability, nuclearity

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Amini, Massoud; Khoshkam, Mahmood. «On nuclearity of the C∗-algebra of an inverse semigroup». Publicacions Matemàtiques, 2020, vol.VOL 64, núm. 2, p. 499–511, http://raco.cat/index.php/PublicacionsMatematiques/article/view/371195.
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