Conjecture on finite-dimensional Fomin–Kirillov algebras for non-exceptional Coxeter groups

Let $G$ be a non-exceptional indecomposable Coxeter group, and let $\mathcal{E}_G$ be its Fomin–Kirillov algebra. Finite-dimensionality conjecture. Up to isomorphism, the only finite-dimensional Fomin–Kirillov algebras $\mathcal{E}_G$ are those for $G=S_2,S_3,S_4,S_5$. The source presents this as an open conjecture derived from the preceding results and from the corresponding classification conjecture for Nichols algebras.