Hou, Bo; Zhang, Zilong; Cai, Bingling; Li, Yan Morita context of weak Hopf algebras. (English) Zbl 1240.16032 Acta Math. Sci., Ser. B, Engl. Ed. 31, No. 3, 1133-1141 (2011). Summary: Let \(H\) be a finite-dimensional weak Hopf algebra and \(A\) a left \(H\)-module algebra with its invariant subalgebra \(A^H\). We prove that the smash product \(A\#H\) is an \(A\)-ring with a grouplike character, and give a criterion for \(A\#H\) to be Frobenius over \(A\). Using the theory of \(A\)-rings, we mainly construct a Morita context \(\langle A^H,A\#H,A,A,\tau,\mu\rangle\) connecting the smash product \(A\#H\) and the invariant subalgebra \(A^H\), which generalizes the corresponding results obtained by M. Cohen, D. Fischman and S. Montgomery [J. Algebra 133, No. 2, 351-372 (1990; Zbl 0706.16023)]. Cited in 1 Document MSC: 16T05 Hopf algebras and their applications 16S40 Smash products of general Hopf actions 16W22 Actions of groups and semigroups; invariant theory (associative rings and algebras) Keywords:weak Hopf algebras; finite-dimensional Hopf algebras; \(H\)-module algebras; rings of invariants; smash products; Morita contexts; \(A\)-rings; Frobenius extensions Citations:Zbl 0706.16023 PDFBibTeX XMLCite \textit{B. Hou} et al., Acta Math. Sci., Ser. B, Engl. Ed. 31, No. 3, 1133--1141 (2011; Zbl 1240.16032) Full Text: DOI