# Beyond recursion operators

@article{KosmannSchwarzbach2019BeyondRO,
title={Beyond recursion operators},
author={Y. Kosmann-Schwarzbach},
journal={arXiv: History and Overview},
year={2019},
pages={167-180}
}
We briefly recall the history of the Nijenhuis torsion of (1, 1)-tensors on manifolds and of the lesser-known Haantjes torsion. We then show how the Haantjes manifolds of Magri and the symplectic Haantjes structures of Tempesta and Tondo generalize the classical approach to integrable systems in the bi-Hamiltonian and symplectic Nijenhuis formalisms, the sequence of powers of the recursion operator being replaced by a family of commuting Haantjes operators.
6 Citations
Higher Haantjes Brackets and Integrability
• Mathematics
• 2018
We propose a new, infinite class of brackets generalizing the Frölicher– Nijenhuis bracket. This class can be reduced to a family of generalized Nijenhuis torsions recently introduced. In particular,Expand
Haantjes Algebras of the Lagrange Top
We study a symplectic-Haantjes manifold and a Poisson–Haantjes manifold for the Lagrange top and compute a set of Darboux–Haantjes coordinates. Such coordinates are separation variables for theExpand
A New Class of Generalized Haantjes Tensors and Nilpotency
• Mathematics
• 2018
We propose a new infinite class of generalized binary tensor fields. The first representative of this class is the known Fr\"olicher--Nijenhuis bracket. Also, this new family of tensors reduces toExpand
Haantjes algebras and diagonalization
• Mathematics, Physics
• 2021
Abstract We introduce the notion of Haantjes algebra: It consists of an assignment of a family of operator fields on a differentiable manifold, each of them with vanishing Haantjes torsion. They areExpand
A New family of higher-order Generalized Haantjes Tensors, Nilpotency and Integrability
• Mathematics
• 2018
We propose a new infinite class of generalized binary tensor fields, whose first representative of is the known Frolicher--Nijenhuis bracket. This new family of tensors reduces to the generalizedExpand

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