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 characteristic 2, simplicity occurs if and only if A is Delta-simple and A(Delta) x Delta = A(Delta)Delta acts faithfully as derivations on A. (C) 1998 Academic Press.