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.

A trihamiltonian extension of the Today lattice

ANDRA', CHIARA;
2007-01-01

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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11579/102166
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