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2020 On nuclearity of the $C^*$-algebra of an inverse semigroup
Massoud Amini, Mahmood Khoshkam
Publ. Mat. 64(2): 499-511 (2020). DOI: 10.5565/PUBLMAT6422005

Abstract

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 $C^*(E_S)$ on the idempotents $E_S$ of $S$ are amenable. Thereby we solve some problems raised by A. L. T. Paterson.

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Massoud Amini. Mahmood Khoshkam. "On nuclearity of the $C^*$-algebra of an inverse semigroup." Publ. Mat. 64 (2) 499 - 511, 2020. https://doi.org/10.5565/PUBLMAT6422005

Information

Received: 19 November 2018; Revised: 27 April 2020; Published: 2020
First available in Project Euclid: 3 July 2020

zbMATH: 07236051
MathSciNet: MR4119951
Digital Object Identifier: 10.5565/PUBLMAT6422005

Subjects:
Primary: 46L57
Secondary: ‎43A07‎

Keywords: amenability , inverse semigroup , nuclearity , universal groupoid

Rights: Copyright © 2020 Universitat Autònoma de Barcelona, Departament de Matemàtiques

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Vol.64 • No. 2 • 2020
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