Failure of flatness over finite-dimensional Hopf subalgebras
Abstract
It is proved in this paper that for any finite-dimensional nonsemisimple Hopf algebra A there exists a Hopf algebra H containing A as a Hopf subalgebra such that H is not flat over A. On the other hand, there is a class of infinite-dimensional Hopf algebras with the property that all Hopf algebras without exception are faithfully flat modules over Hopf subalgebras from this class.
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