Outer Partial Actions and Partial Skew Group Rings

Nystedt, Patrik ; Öinert, Johan

Canadian journal of mathematics, Tome 67 (2015) no. 5, pp. 1144-1160

Résumé

We extend the classical notion of an outer action $\alpha $ of a group $G$ on a unital ring $A$ to the case when $\alpha $ is a partial action on ideals, all of which have local units. We show that if $\alpha $ is an outer partial action of an abelian group $G$ , then its associated partial skew group ring $A\,{{\star }_{\alpha }}\,G$ is simple if and only if $A$ is $G$ -simple. This result is applied to partial skew group rings associated with two different types of partial dynamical systems.

Détail

DOI : 10.4153/CJM-2014-043-8

Mots-clés : 16S35, 16W50, 37B05, 37B99, 54H15, 54H20, outer action, partial action, minimality, topological dynamics, partial skew group ring, simplicity

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