Conformal sl2 enveloping algebras as Ambiskew polynomial rings

We study a three parameter deformation U-abc of U(s[(2)) introduced by Le Bruyn in 1995. Working over an arbitrary algebraically closed field of characteristic zero, we determine the centres, the finite-dimensional irreducible representations, and, when the parameter a is not a non-trivial root of unity, the prime ideals of those U-abc, with ac not equal 0, which are conformal as ambiskew polynomial rings.