Three Graded Modified Classical Yang-Baxter Equations and Integrable Systems

Details Three Graded Modified Classical Yang-Baxter Equations and Integrable Systems Three Graded Modified Classical Yang-Baxter Equations and Integrable Systems

1997-08-11

arxiv.org/abs/solv-int/9708003v1

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, Revtex

Scientific paper

The $6 = 3\times 2$ huge Lie algebra $\Xi$ of all local and non local differential operators on a circle is applied to the standard Adler-Kostant-Symes (AKS) R-bracket sckeme. It is shown in particular that there exist three additional Lie structures, associated to three graded modified classical Yang-Baxter(GMCYB) equations. As we know from the standard case, these structures can be used to classify in a more consitent way a wide class of integrable systems. Other algebraic properties are also presented.

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