Open Access
Winter 2012 Inverse semigroup expansions and their actions on $C^{\ast}$-algebras
Alcides Buss, Ruy Exel
Illinois J. Math. 56(4): 1185-1212 (Winter 2012). DOI: 10.1215/ijm/1399395828


In this work, we give a presentation of the prefix expansion ${\operatorname{\mathbf {Pr}} (G)}$ of an inverse semigroup $G$ as recently introduced by Lawson, Margolis and Steinberg which is similar to the universal inverse semigroup defined by the second named author in case $G$ is a group. The inverse semigroup ${\operatorname{\mathbf {Pr}} (G)}$ classifies the partial actions of $G$ on spaces. We extend this result and prove that Fell bundles over $G$ correspond bijectively to saturated Fell bundles over ${\operatorname{\mathbf {Pr}} (G)}$. In particular, this shows that twisted partial actions of $G$ (on $C^{*}$-algebras) correspond to twisted (global) actions of ${\operatorname{\mathbf {Pr}} (G)}$. Furthermore, we show that this correspondence preserves $C^{*}$-algebra crossed products.


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Alcides Buss. Ruy Exel. "Inverse semigroup expansions and their actions on $C^{\ast}$-algebras." Illinois J. Math. 56 (4) 1185 - 1212, Winter 2012.


Published: Winter 2012
First available in Project Euclid: 6 May 2014

zbMATH: 1298.46053
MathSciNet: MR3231479
Digital Object Identifier: 10.1215/ijm/1399395828

Primary: 20M18 , 20M30 , 46L55

Rights: Copyright © 2012 University of Illinois at Urbana-Champaign

Vol.56 • No. 4 • Winter 2012
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