The structure theorem of endomorphism algebras for weak Doi-Hopf modules.
The paper presents some structure properties of the weak Doi-Hopf modules. Using the condition of weak Hopf-Galois extension, the authors prove the following main result (Theorem 2.8): if \(H\) is a finite dimensional weak Hopf algebra, \(A/B\) is a weak right \(H\)-Galois extension and \(M\) is a weak Doi-Hopf module, then the smash product between the algebra of \(A\)-endomorphisms of \(M\) and \(H^*\) is isomorphic as an algebra with the algebra of \(B\)-endomorphisms of \(M\). By applying this theorem, they obtain the Kreimer-Takeuchi theorem [see \textit{H. F. Kreimer} and \textit{M. Takeuchi}, Indiana Univ. Math. J. 30, 675-692 (1981; Zbl 0451.16005)] and the Nikshych duality theorem for smash products in the case of weak Hopf algebras [see \textit{D. Nikshych}, Contemp. Math. 267, 237-243 (2000; Zbl 0978.16032)].
scientific article; zbMATH DE number 5881186
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