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Algebraic Nijenhuis operators and Kronecker Poisson pencils

Andriy Panasyuk
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Abstract

We give a criterion of (micro-)kroneckerity of the linear Poisson pencil on $\frak{g}^*$ related to an algebraic Nijenhuis operator $N:\frak{g}\to \frak{g}$ on a finite-dimensional Lie algebra $\frak{g}$. As an application we get a series of examples of completely integrable systems on semisimple Lie algebras related to Borel subalgebras and a new proof of the complete integrability of the free rigid body system on $\frak{gl}_n$.

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Andriy Panasyuk. 2005-05-19. Algebraic Nijenhuis operators and Kronecker Poisson pencils. https://arxiv.org/abs/math/0504337

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