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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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