A trihamiltonian extension of the Toda lattice
  A new Poisson structure on a subspace of the Kupershmidt algebra is defined. This Poisson structure, together with other two already known, allows to construct a trihamiltonian recurrence for an extension of the periodic Toda lattice with $n$ particles. Some explicit examples of the construction and of the first integrals found in this way are given. 
Chiara Andr\`a, Luca Degiovanni, Guido Magnano