Cosemisimple Hopf algebras are faithfully flat over Hopf subalgebras

Details Cosemisimple Hopf algebras are faithfully flat over Hopf subalgebras Cosemisimple Hopf algebras are faithfully flat over Hopf subalgebras

2011-10-31

arxiv.org/abs/1110.6701v1

Mathematics

Rings and Algebras

14 pages + references; TikZ diagrams

Scientific paper

The question of whether or not a Hopf algebra $H$ is faithfully flat over a Hopf subalgebra $A$ has received positive answers in several particular cases: when $H$ (or more generally, just $A$) is commutative, or cocommutative, or pointed, or when $K$ contains the coradical of $H$. We prove the statement in the title, adding the class of cosemisimple Hopf algebras to those known to be faithfully flat over all Hopf subalgebras. We also show that the third term of the resulting "exact sequence" $A\to H\to C$ is always a cosemisimple coalgebra.

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