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Correspondence theorems for Hopf algebroids with applications to affine groupoids

par El Kaoutit, L.;Ghobadi, Aryan;Saracco, Paolo ;Vercruysse, Joost
Référence Canadian journal of mathematics, page (1-51)
Publication Publié, 2023-04

Article révisé par les pairs

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Résumé :

We provide a correspondence between one-sided coideal subrings and one-sided ideal two-sided coideals in an arbitrary bialgebroid. We prove that, under some expected additional conditions, this correspondence becomes bijective for Hopf algebroids. As an application, we investigate normal Hopf ideals in commutative Hopf algebroids (affine groupoid schemes) in connection with the study of normal affine subgroupoids.