Quasigraded Lie Algebras and Modified Toda Field Equations

Abstract

We construct a family of quasigraded Lie algebras that coincide with the deformations of the loop algebras in "principal" gradation and admit Kostant-Adler-Symes scheme. Using them we obtain new Volterra coupled systems and modified Toda field equations for all series of classical matrix Lie algebras $\mathfrak{g}$.

Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

Cited by in corpus (1)

• Classical R-matrix theory for bi-Hamiltonian field systems