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Partial corepresentations of Hopf algebras

par Alves, Marcelo Muniz S;Batista, Eliezer;Castro, Felipe;Quadros, Glauber;Vercruysse, Joost
Référence Journal of algebra, 577, page (74-135)
Publication Publié, 2021-07-01

Article révisé par les pairs

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Résumé :

We introduce the notion of a partial corepresentation of a given Hopf algebra H over a coalgebra C and the closely related concept of a partial H-comodule. We prove that there exists a universal coalgebra Hpar, associated to the original Hopf algebra H, such that the category of regular partial H-comodules is isomorphic to the category of Hpar-comodules. We introduce the notion of a Hopf coalgebroid and show that the universal coalgebra Hpar has the structure of a Hopf coalgebroid over a suitable coalgebra.