Correspondence theorems for Hopf algebroids with applications to affine groupoids
Rings and Algebras
2023-09-11 v1 Algebraic Geometry
Quantum Algebra
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.
Cite
@article{arxiv.2211.07756,
title = {Correspondence theorems for Hopf algebroids with applications to affine groupoids},
author = {Laiachi El Kaoutit and Aryan Ghobadi and Paolo Saracco and Joost Vercruysse},
journal= {arXiv preprint arXiv:2211.07756},
year = {2023}
}