Abstract :
LetKbe a field, letAbe an associative, commutativeK-algebra, and let Δ be a nonzeroK-vector space of commutingK-derivations ofA. Then, with a rather natural definition,A K Δ = AΔ 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 ifAis Δ-simple andAΔ Δ = AΔΔ acts faithfully as derivations onA.
