Morita equivalence of partial group actions and globalization

Abstract

We consider a large class of partial actions of groups on rings, called regular, which contains all s-unital partial actions, as well as all partial actions on C∗-algebras. For them the notion of Morita equivalence is introduced, and it is shown that any regular partial action is Morita equivalent to a globalizable one, and the globalization is essentially unique. It is also proved that Morita equivalent s-unital partial actions on rings with orthogonal local units are stably isomorphic. In addition, we show that Morita equivalent s-unital partial actions on commutative rings must be isomorphic, and an analogous result for C∗-algebras is also established. Date: November 8, 2015. This work was partially supported by CNPq of Brazil (Proc. 305975/2013-7, Proc. 300362/20102), Fapesp of Brazil (Proc. Proc. 2009/52665-0), MINECO (Ministerio de Economia y Competitividad), (Fondo Europeo de Desarrollo Regional) project MTM2012-35240, Spain, and Fundacion Seneca of Murcia, Programa Hispano Brasileno de Cooperacion Universitaria PHB2012-0135, Spain. 2000 Mathematics Subject Classification: Primary 16S35; Secondary 16W22, 46L05.