L. Vendramin

Finite-dimensional pointed Hopf algebras with alternating groups are trivial

It is shown that Nichols algebras over alternating groups

Skew braces and the Yang–Baxter equation

{\mathbb A_m}

Extensions of set-theoretic solutions of the Yang–Baxter equation and a conjecture of Gateva-Ivanova

(m ≥ 5) are infinite dimensional. This proves that any complex finite dimensional pointed Hopf algebra with group of group-likes isomorphic to

Braided racks, Hurwitz actions and Nichols algebras with many cubic relations

{\mathbb A_m}

Hopf braces and Yang-Baxter operators

is isomorphic to the group algebra. In a similar fashion, it is shown that the Nichols algebras over the symmetric groups