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Correspondence theorems for Hopf algebroids with applications to affine groupoids

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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… Click to show full abstract

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.

Keywords: correspondence theorems; hopf algebroids; correspondence; applications affine; theorems hopf; algebroids applications

Journal Title: Canadian Journal of Mathematics
Year Published: 2022

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