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Supramenable groups and partial actions

Published online by Cambridge University Press:  28 January 2016

EDUARDO P. SCARPARO
EDUARDO P. SCARPARO*
Affiliation:
Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark email duduscarparo@gmail.com
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Abstract

We characterize supramenable groups in terms of the existence of invariant probability measures for partial actions on compact Hausdorff spaces and the existence of tracial states on partial crossed products. These characterizations show that, in general, one cannot decompose a partial crossed product of a $\text{C}^{\ast }$-algebra by a semidirect product of groups into two iterated partial crossed products. However, we give conditions which ensure that such decomposition is possible.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 37 , Issue 5 , August 2017 , pp. 1592 - 1606
Copyright
© Cambridge University Press, 2016 

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