Abstract
In this paper, we give a necessary and sufficient condition for a comodule algebra over a weak Hopf algebra to have a total integral, thus extending the classical theory developed by Doi in the Hopf algebra setting. Also, from these results, we deduce a version of Maschke’s Theorem for (H,B)-Hopf modules associated with a weak Hopf algebra H and a right H-comodule algebra B.
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