SIMPLE LIE-ALGEBRAS OF WITT TYPE

Let K be a field, let A be an associative, commutative K-algebra, and let Delta be a nonzero K-vector space of commuting K-derivations of A. Then, with a rather natural definition, A x(K) Delta =A Delta becomes a Lie algebra and we obtain necessary and sufficient conditions here for this Lie algebra to be simple. With one minor exception in charact eristic 2, simplicity occurs if and only if A is Delta-simple and A(De lta) x Delta = A(Delta)Delta acts faithfully as derivations on A. (C) 1998 Academic Press.