Abstract
We give a coring version for the duality theorem for actions and coactions of a finitely generated projective Hopf algebra. We also provide a coring analogue for a theorem of H.-J. Schneider, which generalizes and unifies the duality theorem for finite Hopf algebras and its refinements.
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Blattner, R.J., Montgomery, S.: A duality theorem for Hopf module algebras. J. Algebra 95(1), 153–172 (1985)
Brzeziński, T., Wisbauer, R.: Corings and comodules. In: London Mathematical Society. Lecture Note Series, vol. 309, Cambridge University Press, Cambridge, UK (2003)
Dăscălescu, S., Năstăsescu, C., Raianu, Ş.: Hopf algebras: an introduction. In: Monographs and Textbooks in Pure and Applied Mathematics, vol. 235, Marcel Dekker, New York (2001)
Dăscălescu, S., Raianu, Ş., Van Oystaeyen, F.: Some remarks on a theorem of H.-J. Schneider. Comm. Algebra 24(14), 4477–4493 (1996)
Menini, C., Raianu, Ş.: Morphisms of relative Hopf modules, smash products and duality. J. Algebra 219, 547–570 (1999)
Montgomery, S.: Hopf algebras and their actions on rings. In: CBMS Regional Conference Series in Mathematics, vol. 82, American Mathematical Society, Providence, RI (1993)
Schneider, H.-J.: Hopf Galois extensions, crossed products and Clifford theory. In: Bergen, J., Montgomery, S. (eds.) Advances in Hopf Algebras. Lecture Notes in Pure and Applied Mathematics, vol. 158, pp. 267–298, Marcel Dekker, New York (1994)
Sweedler, M.E.: Hopf Algebras. Benjamin, New York (1969)
Sweedler, M.E.: The predual theorem to the Jacobson–Bourbaki theorem. Trans. Amer. Math. Soc. 213, 391–406 (1975)
Ulbrich, K.-H.: Smash products and comodules of linear maps. Tsukuba J. Math. 14, 371–378 (1990)
Van den Bergh, M.: A duality theorem for Hopf algebras. In: Methods in Ring Theory, Antwerp, 1983, pp. 517–522. NATO Advanced Study Institutes Series. Series C, Mathematical and Physical Sciences, vol. 129, Reidel, Dordrecht, The Netherlands (1984)
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This paper was written while the first author visited the Mathematics Departments of Syracuse University and California State University Dominguez Hills. He would like to thank both departments for their hospitality.
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Caenepeel, S., Quinn, D. & Raianu, Ş. Duality for Finite Hopf Algebras Explained by Corings. Appl Categor Struct 14, 531–537 (2006). https://doi.org/10.1007/s10485-006-9046-3
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DOI: https://doi.org/10.1007/s10485-006-9046-3