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

• Autores: Massoud Amini, Mahmood Khoshkam
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 64, Nº 2, 2020, págs. 499-511
• Idioma: inglés
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• Resumen

  • 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.