6 problems

Let $H$ be a right noetherian Hopf algebra over a field, and let $S$ denote its antipode. Skryabin's bijective antipode conjecture. The antipode $S$ is bijective. Skryabin proved t…

Radford–Schneider order-divisibility conjectural consequence. Assuming the strong vanishing trace conjecture, the order of $S^2$ divides

Radford–Schneider strong vanishing trace conjecture. The square of the antipode $S^2$ satisfies the strong vanishing trace condition.

Antipode formula for the socle. The coproduct of the socle element should satisfy

Let $\textbf{\textsc{pre}}^\natural$ denote the Hopf monoid arising from a Hopf class; equivalently, consider every Hopf monoid arising from a Hopf class. Multiplicity-freeness con…

Let the universal Hopf class be denoted by $\textbf{\textsc{pre}}$. Multiplicity-freeness conjecture. The antipode for the Hopf monoid of the universal Hopf class…