The finite simple group conjecture for pointed Hopf algebras

Let $\boldsymbol{G}$ be a finite simple non-abelian group. A complex Yetter–Drinfeld module $V$ of $\boldsymbol{G}$ has an associated Nichols algebra $\mathfrak B(V)$. Finite simple group conjecture. For every such $V$,

$$\dim\mathfrak B(V)=\infty.$$

Consequently, the only finite-dimensional complex pointed Hopf algebra whose group of grouplikes is $\boldsymbol{G}$ should be the group algebra

$$\mathbb{C}\boldsymbol{G}.$$

This is a folklore conjecture motivated by the classification of finite-dimensional Nichols algebras over finite simple groups; the paper proves the asserted consequence for the simple Suzuki and Ree groups, while the conjecture in general remains open.