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Globalization of twisted partial Hopf actions. (English) Zbl 1381.16032

The paper under review is a natural continuation of a previous work by the authors [Isr. J. Math. 197, 263–308 (2013; Zbl 1287.16028)]. Now they give necessary and sufficient conditions for a twisted partial action to have a globalization. The main result establishes the following: a symmetric twisted partial action of a Hopf algebra \(H\) on a unital algebra \(A\) associated to the symmetric pair of partial cocycles \(\omega\) and \(\omega '\) is globalizable if and only if there exists a normalized convolution invertible linear map \(\tilde{\omega}:H\otimes H\rightarrow A\) satisfying certain compatibility conditions for intertwining the partial action of \(H\) on \(A\) and the restriction of the twisted action of \(H\) on \(B\).

MSC:

16T05 Hopf algebras and their applications
16S40 Smash products of general Hopf actions

Citations:

Zbl 1287.16028
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