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Integrable hierarchies and the modular class

Pantelis A. Damianou·Rui Loja Fernandes
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Abstract

We observe that the modular class of a Poisson-Nijhenhuis manifold has a canonical representative and that, under a cohomological assumption, this vector field is bi-hamiltonian. In many examples the associated hierarchy of flows reproduces classical integrable hierarchies.

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Pantelis A. Damianou, Rui Loja Fernandes. 2006-10-11. Integrable hierarchies and the modular class. https://arxiv.org/abs/math/0607784

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