2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/106467A 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.24 pagesExactly Solvable and Integrable Systemstext