Globalization of twisted partial actions

Dokuchaev, M.; Exel, R.; Simón, J.

doi:10.1090/S0002-9947-10-04957-3

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.

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