On the Lorenzoni-Magri hierarchy of hydrodynamic type

In 2005 Lorenzoni and Magri showed that a hydrodynamic-type hierarchy determined by the powers of a type (1,1) tensor field (on a smooth manifold) with vanishing Nijenhuis torsion can be deformed to a more general hierarchy, with the help of a chain of conservation laws of the new hierarchy. We review this construction. The (1,1) tensor fields of the resulting hierarchy have non-vanishing Nijenhuis torsion, in general, but their Haantjes tensor vanishes.
Comment: 12 pages, third version: Proposition 3.1 in previous versions was incorrect and has been deleted, Theorem 4.5 follows directly from a result of Bogoyavlenskij in 2004, corresponding note added at the end of the paper