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Linear Nijenhuis-Tensors and the Construction of Integrable Systems

Axel Winterhalder
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Abstract

A new method to construct Hamiltonian functions in involution is presented. We show that on left-symmetric algebras a Nijenhuis-tensor is given in a natural manner by the usual right-multiplication. Furthermore we prove that symplectic Lie-algebras carry the structure of a Poisson-Nijenhuis manifold.

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Axel Winterhalder. 1997-09-04. Linear Nijenhuis-Tensors and the Construction of Integrable Systems. https://arxiv.org/abs/physics/9709008

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