Globalization of twisted partial actions
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- by M. Dokuchaev, R. Exel and J. J. Simón PDF
- Trans. Amer. Math. Soc. 362 (2010), 4137-4160 Request permission
Abstract:
Let $\mathcal {A}$ be a unital ring which is a product of possibly infinitely many indecomposable rings. We establish a criteria for the existence of a globalization for a given twisted partial action of a group on $\mathcal {A}.$ If the globalization exists, it is unique up to a certain equivalence relation and, moreover, the crossed product corresponding to the twisted partial action is Morita equivalent to that corresponding to its globalization. For arbitrary unital rings the globalization problem is reduced to an extendibility property of the multipliers involved in the twisted partial action.References
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Additional Information
- M. Dokuchaev
- Affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, 05508-090 São Paulo, SP, Brazil
- 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, Brazil
- MR Author ID: 239607
- Email: exel@mtm.ufsc.br
- J. J. Simón
- Affiliation: Departamento de Matemáticas, Universidad de Murcia, 30071 Murcia, España
- Email: jsimon@um.es
- Received by editor(s): February 15, 2008
- Published electronically: March 24, 2010
- Additional Notes: This work was partially supported by CNPq of Brazil and Secretaría de Estado de Universidades e Investigación del MEC, España
- © Copyright 2010 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 362 (2010), 4137-4160
- MSC (2010): Primary 16W50; Secondary 16S35, 16W22
- DOI: https://doi.org/10.1090/S0002-9947-10-04957-3
- MathSciNet review: 2608399