Geodesic
Correspondence theorems for Hopf algebroids with applications to affine groupoids
Canadian journal of mathematics, Tome 76 (2024) no. 3, pp. 830-880

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DOI

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.
DOI : 10.4153/S0008414X23000238
Mots-clés : Hopf algebroids, normal ideals, affine groupoids, normal affine subgroupoids, comodule algebras, finite groupoids, Hopf algebroids of functions, Galois correspondence 
Kaoutit, Laiachi El; Ghobadi, Aryan; Saracco, Paolo; Vercruysse, Joost. Correspondence theorems for Hopf algebroids with applications to affine groupoids. Canadian journal of mathematics, Tome 76 (2024) no. 3, pp. 830-880. doi: 10.4153/S0008414X23000238
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     author = {Kaoutit, Laiachi El and Ghobadi, Aryan and Saracco, Paolo and Vercruysse, Joost},
     title = {Correspondence theorems for {Hopf} algebroids with applications to affine groupoids},
     journal = {Canadian journal of mathematics},
     pages = {830--880},
     year = {2024},
     volume = {76},
     number = {3},
     doi = {10.4153/S0008414X23000238},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X23000238/}
}
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