Integrable hierarchies and the modular class

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.

26 pages, 27 references. One major change: the assumption on non-degeneracy of the Poisson tensor on a PN manifold was dropped. Several minor changes and 2 new references included

References in corpus (1)

• Multiple Hamiltonian structure of Bogoyavlensky-Toda lattices

Cited by in corpus (2)

• Jacobi-Nijenhuis algebroids and their modular classes
• The Van den Bergh duality and the modular symmetry of a Poisson variety