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Amenable actions of inverse semigroups

Published online by Cambridge University Press:  06 October 2015

RUY EXEL  and
CHARLES STARLING
RUY EXEL
Affiliation:
Universidade Federal de Santa Catarina, Departamento de Matemática, Florianópolis, Brazil
CHARLES STARLING
Affiliation:
University of Ottawa, Department of Mathematics and Statistics, Ottawa, Canada email [email protected]
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Abstract

We say that an action of a countable discrete inverse semigroup on a locally compact Hausdorff space is amenable if its groupoid of germs is amenable in the sense of Anantharaman-Delaroche and Renault. We then show that for a given inverse semigroup ${\mathcal{S}}$, the action of ${\mathcal{S}}$ on its spectrum is amenable if and only if every action of ${\mathcal{S}}$ is amenable.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 37 , Issue 2 , April 2017 , pp. 481 - 489
Copyright
© Cambridge University Press, 2015 

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References

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