Delta Methods in Enveloping Rings, II Original Research Article

Let L be a Lie algebra over a field K of characteristic 0 and define ΔL to be the join of all finite-dimensional Lie ideals of L. Then ΔL is a characteristic ideal of L which can be appreciably smaller than the ideal Δ = {l set membership, variant L dimK [l, L] < ∞ }. In a previous paper the authors showed that the linear identities in a twisted smash product R#U(L) are all controlled by Δ. Here we sharpen the result by proving that these identities are in fact controlled by the ideal ΔL.