Three Graded Modified Classical Yang-Baxter Equations and Integrable Systems

Abstract

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.

22 pages, Revtex

References in corpus (1)

• R-Matrix Formulation of KP Hierarchies and their Gauge Equivalence