A Further Generalization of Algebras of Cartan Type W

AbstractIn this paper, a class of infinite-dimensional Lie algebras, called algebras of Cartan type W̃*, over a field F of characteristic 0 is studied. These algebras are derivations of the field F(x1,x2,…,xn). We prove that algebras of Cartan type W̃* are simple. We also prove that any derivation on an algebra of this type with one indeterminate is an inner derivation