“…Since we are in characteristic 0, a special case of the Cartier-Gabriel-Kostant theorem, [Mon,Theorem 5.6.5], ensures that H is the enveloping algebra of the Lie algebra P (H) = i = 1 n kx i . Conversely, suppose that H is an IHOE which is isomorphic as Hopf algebra to the enveloping algebra of the Lie algebra g. We claim that H can be realised as an IHOE with a basis of g as the set of skew polynomial generators of H. Argue by induction on n := GKdimH = dim k g, the second equality holding by [KL,Example 6.9]. By hypothesis, H = T [x; σ, δ] for an IHOE T , with GKdimT = n−1, by Corollary (2.8).…”