Simple Lie algebras of Witt-type

Abstract. Let K be a eld, let A be an associative, commutative K-algebra and let be a nonzero K-vector space of commuting K-derivations of A. Then, with a rather natural denition, A K = A becomes a Lie algebra, and we obtain necessary and sucient conditions here for this Lie algebra to be simple. With one minor exception in characteristic 2, simplicity occurs if and only if A is -simple and A = A acts faithfully as derivations on A. Let K be a eld, let A be an associative, commutative K-algebra and let be a nonzero K-vector space of commuting K-derivations of A. Then the tensor produc