Morita equivalence of partial group actions and globalization
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- by F. Abadie, M. Dokuchaev, R. Exel and J. J. Simón PDF
- Trans. Amer. Math. Soc. 368 (2016), 4957-4992 Request permission
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 $C^{\ast }$-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 that 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 $C^{\ast }$-algebras is also established.References
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Additional Information
- F. Abadie
- Affiliation: Centro de Matemática, Facultad de Ciencias, Universidad de la República, Iguá 4225, CP 11400, Montevideo, Uruguay
- Email: fabadie@cmat.edu.uy
- M. Dokuchaev
- Affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, 05508-090 São Paulo, SP, Brasil
- MR Author ID: 231275
- ORCID: 0000-0003-1250-4831
- Email: dokucha@ime.usp.br
- R. Exel
- Affiliation: Departamento de Matemática, Universidade Federal de Santa Catarina, 88040-900 Florianópolis, SC, Brasil
- MR Author ID: 239607
- Email: exel@mtm.ufsc.br
- J. J. Simón
- Affiliation: Departamento de Matemáticas, Universidad de Murcia, 30071 Murcia, España
- ORCID: 0000-0001-6362-189X
- Email: jsimon@um.es
- Received by editor(s): June 5, 2013
- Received by editor(s) in revised form: June 2, 2014
- Published electronically: November 6, 2015
- Additional Notes: This work was partially supported by CNPq of Brazil (Proc. 305975/2013-7, Proc. 300362/2010-2), Fapesp of Brazil (Proc. Proc. 2009/52665-0), MINECO (Ministerio de Economía y Competitividad), (Fondo Europeo de Desarrollo Regional) project MTM2012-35240, Spain, and Fundación Séneca of Murcia, Programa Hispano Brasileño de Cooperación Universitaria PHB2012-0135, Spain
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 4957-4992
- MSC (2010): Primary 16S35; Secondary 16W22, 46L05
- DOI: https://doi.org/10.1090/tran/6525
- MathSciNet review: 3456167