The structure theorem for comodule algebras over Hopf algebroids.
\textit{G. Militaru} and \textit{D. Stefan} [Commun. Algebra 22, No. 14, 5657-5678 (1994; Zbl 0816.16029)] showed that comodule algebras over Hopf algebras are smash products if and only if there exists a comodule algebra morphism from the Hopf algebra to the comodule algebra. Later this was generalized to comodule algebras over quasi-Hopf algebras [\textit{F. Panaite} and \textit{F. Van Oystaeyen}, Proc. Am. Math. Soc. 135, No. 6, 1669-1677 (2007; Zbl 1160.16021)]. The goal of the paper under review is to generalize this even further to comodule algebras over Hopf algebroids. The main tool is a structure theorem for \((H,\mathcal H)\)-Hopf bimodules, where \(\mathcal H\) is a Hopf algebroid on the total Hopf algebra \(H\).
scientific article; zbMATH DE number 6006424
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