Displaying similar documents to “On Lax pairs and matrix extended simple Toda systems.”

Integrable three-dimensional coupled nonlinear dynamical systems related to centrally extended operator Lie algebras and their Lax type three-linearization

J. Golenia, O. Hentosh, A. Prykarpatsky (2007)

Open Mathematics

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The Hamiltonian representation for a hierarchy of Lax type equations on a dual space to the Lie algebra of integro-differential operators with matrix coefficients, extended by evolutions for eigenfunctions and adjoint eigenfunctions of the corresponding spectral problems, is obtained via some special Bäcklund transformation. The connection of this hierarchy with integrable by Lax two-dimensional Davey-Stewartson type systems is studied.

Dirac structures and dynamical r -matrices

Zhang-Ju Liu, Ping Xu (2001)

Annales de l’institut Fourier

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The purpose of this paper is to establish a connection between various objects such as dynamical r -matrices, Lie bialgebroids, and Lagrangian subalgebras. Our method relies on the theory of Dirac structures and Courant algebroids. In particular, we give a new method of classifying dynamical r -matrices of simple Lie algebras 𝔤 , and prove that dynamical r -matrices are in one-one correspondence with certain Lagrangian subalgebras of 𝔤 ⊕ 𝔤 .

Deformation on phase space.

Oscar Arratia, M.ª Angeles Martín Mínguez, María Angeles del Olmo (2002)

RACSAM

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El trabajo que presentamos constituye una revisión de varios procedimientos de cuantización basados en un espacio de fases clásico M. Estos métodos consideran a la mecánica cuántica como una "deformación" de la mecánica clásica por medio de la "transformación" del álgebra conmutativa C(M) en una nueva álgebra no conmutativa C(M). Todas estas ideas conducen de modo natural a los grupos cuánticos como deformación (o cuantización en un sentido amplio) de los grupos de Poisson-Lie, lo cual...