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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Globalization of twisted partial actions


Authors: M. Dokuchaev, R. Exel and J. J. Simón
Journal: Trans. Amer. Math. Soc. 362 (2010), 4137-4160
MSC (2010): Primary 16W50; Secondary 16S35, 16W22
Published electronically: March 24, 2010
MathSciNet review: 2608399
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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.


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Additional Information

M. Dokuchaev
Affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, 05508-090 São Paulo, SP, Brazil
Email: dokucha@ime.usp.br

R. Exel
Affiliation: Departamento de Matemática, Universidade Federal de Santa Catarina, 88040-900 Florianópolis, SC, Brazil
Email: exel@mtm.ufsc.br

J. J. Simón
Affiliation: Departamento de Matemáticas, Universidad de Murcia, 30071 Murcia, España
Email: jsimon@um.es

DOI: http://dx.doi.org/10.1090/S0002-9947-10-04957-3
PII: S 0002-9947(10)04957-3
Keywords: Partial action, twisting, crossed product, globalization
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
Article copyright: © Copyright 2010 American Mathematical Society