AUTOMORPHISMS AND TWISTED FORMS OF GENERALIZED WITT LIE-ALGEBRAS

We prove that the automorphisms of the generalized Witt Lie algebras W(m, n) over arbitrary commutative rings of characteristic p greater-than-or-equal-to 3 all come from automorphisms of the algebras on which they are defined as derivations. By descent theory, this result then implies that if a Lie algebra over a field becomes isomorphic to W(m, n) over the algebraic closure, it is a derivation algebra of the type studied long ago by Ree. Furthermore, all isomorphisms of those derivation algebras are induced by isomorphisms of their underlying associative algebras.