Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 2 (2006), 043, 14 pages      nlin.SI/0604032      https://doi.org/10.3842/SIGMA.2006.043

Quasigraded Lie Algebras and Modified Toda Field Equations

Taras V. Skrypnyk a, b
a) Bogolyubov Institute for Theoretical Physics, 14-b Metrologichna Str., Kyiv, 03143 Ukraine
b) Institute of Mathematics, 3 Tereshchenkivs'ka Str., Kyiv-4, 01601 Ukraine

Received October 31, 2005, in final form March 03, 2006; Published online April 16, 2006

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 g.

Key words: infinite-dimensional Lie algebras; soliton equations.

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