Skryabin's bijective antipode conjecture for noetherian Hopf algebras

Let $H$ be a noetherian Hopf algebra, and let $S$ denote its antipode. Skryabin's conjecture. The antipode $S$ of every noetherian Hopf algebra is bijective. Bijectivity is known for finite-dimensional Hopf algebras, commutative or cocommutative Hopf algebras, and several classes of noetherian Hopf algebras, but the general noetherian case remains open.