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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 cstar050@uottawa.ca
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Abstract

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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.

Information

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

References

Anantharaman-Delaroche, C.. Amenability and exactness for dynamical systems and their C*-algebras. Trans. Amer. Math. Soc. 354 (2002), 4153–4178.CrossRefGoogle Scholar
Anantharaman-Delaroche, C. and Renault, J.. Amenable Groupoids (Monographie de l’Enseignement Mathématique, 36) . l’Enseignement Mathématique, Geneva, 2000.Google Scholar
Duncan, J. and Paterson, A.. C*-algebras of inverse semigroups. Proc. Edinb. Math. Soc. 28 (1985), 4158.Google Scholar
Exel, R.. Inverse semigroups and combinatorial C*-algebras. Bull. Braz. Math. Soc. (N.S.) 39(2) (2008), 191–313.Google Scholar
Milan, D.. C*-algebras of inverse semigroups: amenability and weak containment. J. Operator Theory 63(2) (2010), 317–332.Google Scholar
Paterson, A.. Groupoids, Inverse Semigroups, and Their Operator Algebras. Birkhäuser, Boston, MA, 1999.Google Scholar
Renault, J.. A Groupoid Approach to C*-algebras (Lecture Notes in Mathematics, 793) . Springer, Berlin, 1980.CrossRefGoogle Scholar
Willett, R.. A non-amenable groupoid whose maximal and reduced C*-algebras are the same. Preprint, 2015, arXiv:1504.05615 [math.OA].Google Scholar