A further generalization of algebras of Cartan type \(W\)
Over a field \(F\) of characteristic 0, the author extends the (infinite-dimensional) Lie algebra of Cartan type \(W\), which is by definition the derivation algebra of the polynomial algebra (of \(n\) indeterminates), to the Lie algebra \(\widetilde{W}^*:= \operatorname {Der} F(x_1,\dots, x_n)\), the derivation algebra of the algebra of rational functions. The author shows that \(\widetilde{W}^*\) is simple. When \(n=1\), it is proved that every derivation of \(\widetilde{W}^*\) is inner.
scientific article; zbMATH DE number 1423884