Flatness of Noetherian Hopf algebras over coideal subalgebras
Rings and Algebras
2020-01-10 v1
Abstract
It is proved in the paper that a Noetherian residually finite dimensional Hopf algebra is a flat module over any right Noetherian right coideal subalgebra. In the case of Hopf subalgebras we get faithful flatness. These results are obtained by verifying the existence of the classical quotient rings of those algebras. It is also proved that the antipode of either right or left Noetherian residually finite dimensional Hopf algebra is bijective. As a consequence, such a Hopf algebra is right and left Noetherian simultaneously.
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Cite
@article{arxiv.2001.02848,
title = {Flatness of Noetherian Hopf algebras over coideal subalgebras},
author = {Serge Skryabin},
journal= {arXiv preprint arXiv:2001.02848},
year = {2020}
}
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