  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.
