ON THE STABLE DERIVATION ALGEBRA ASSOCIATED WITH SOME BRAID-GROUPS

We shall prove some stability property of the graded Lie algebra D(n) of certain derivations associated with pure sphere braid group on n strings; in fact, that D(n) congruent-to D5 for n greater-than-or-equal-to 6. These Lie algebras D(n) are connected with some big l-adic Galois representations, and the stability property is related to some conjecture of Grothendieck.