Simple Lie algebras of Witt type (Q1270088)

Let \(K\) be a field, \(A\) an associative commutative \(K\)-algebra and \(\Delta\) a nonzero \(K\)-vector space of commuting \(K\)-derivations of \(A\). Then \(A \otimes_K \Delta= A\Delta\) becomes a Lie algebra. The author obtains necessary and sufficient conditions for \(A\Delta\) to be simple. With one minor exception in characteristic 2, simplicity occurs if and only if \(A\) is \(\Delta\)-simple and \(A^\Delta \otimes \Delta= A^\Delta \Delta\) acts faithfully as derivations on \(A\).