A trihamiltonian extension of the Toda lattice |
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Authors: | Chiara Andrà Luca Degiovanni Guido Magnano |
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Institution: | Dipartimento di Matematica, Università di Torino, via Carlo Alberto 10, I-10123 Torino, Italy |
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Abstract: | A new Poisson structure is defined on a subspace of the Kupershmidt algebra, isomorphic to the space H of n×n Hermitian matrices. The new Poisson structure is of Lie–Poisson type with respect to the standard Lie bracket of H. This Poisson structure (together with two already known ones, obtained through a r-matrix technique) allows to construct an extension of the periodic Toda lattice with n particles that fits in a trihamiltonian recurrence scheme. Some explicit examples of the construction and of the first integrals found in this way are given. |
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Keywords: | Classical integrable systems Symplectic geometry |
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