A Maschke type theorem for weak Hopf algebras. (Q960639)
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scientific article; zbMATH DE number 5485352
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A Maschke type theorem for weak Hopf algebras. |
scientific article; zbMATH DE number 5485352 |
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A Maschke type theorem for weak Hopf algebras. (English)
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5 January 2009
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Total integrals were introduced by \textit{Y. Doi} [Commun. Algebra 13, 2137-2159 (1985; Zbl 0576.16004)]. In this paper, the authors generalize Doi's results to weak Hopf algebras in symmetric monoidal categories admitting split idempotents. One of the results, Theorem 1.7, is the following: if \(H\) is a weak Hopf algebra and \(B\) is a right \(H\)-comodule algebra, then there exists a total integral \(\gamma\colon H\to B\) if and only if \(B\) is relative injective as an \(H\)-comodule. Other equivalent characterizations are given.
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monoidal categories
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weak Hopf algebras
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Hopf modules
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Maschke theorem
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total integrals
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comodule algebras
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