Faithful flatness of Hopf algebras over coideal subalgebras with a bimodule conditional expectation

Abstract

We give a direct and self-contained proof that if $H$ is a Hopf algebra and $A\subset H$ is a right coideal subalgebra such $A$ is a direct summand in $H$ as an $A$-bimodule, then $H$ is faithfully flat as a left and right $A$-module.

B. Mesablishvili pointed out an error in the proof of the main result of the previous version, and a recent paper of S. Skryabin shows that the error cannot be repaired. The paper now gives a self-contained proof of a weaker result, which is reflected in the new title