Vanishing Haantjes tensor conjecture for dispersionless systems from Novikov algebras

Let $\mathbb{A}_n$ be a Novikov algebra, and let the associated equations of hydrodynamic type be the dispersionless systems constructed from that algebra, such as the system described above. Vanishing Haantjes tensor conjecture. The equations of hydrodynamic type constructed from an arbitrary Novikov algebra have vanishing Haantjes tensor. The paper proves vanishing of the Haantjes tensor for the explicitly constructed Novikov algebras and notes that the characteristic speeds are distinct in dimensions $n=2,3,4$; the conjectured extension to arbitrary Novikov algebras remains open.