X-inner automorphisms of enveloping rings

In this paper, we determine the X-inner automorphisms of the smash product R # U(L) of a prime ring R by the universal enveloping algebra U(L) of a characteristic 0 Lie algebra L. Specifically, we show that any such automorphism σ stabilizing R can be written as a product σ = σ₁σ₂, where σ₁ is induced by conjugation by a unit of Q₃(R), the symmetric Martindale ring of quotients of R, and σ₂ is induced by conjugation by a unit of Q₃(T). Here S = Q_l(R) is the left Martindale ring of quotients of R and T is the centralizer of S in S # U(L) - R # U(L). One of the subtleties of the proof is that we must work in several unrelated overrings of R # U(L).