Complete primeness of prime ideals in the one-sided Witt enveloping algebra

Prove that every prime ideal of the universal enveloping algebra U(W_{a0-1}) is completely prime.

Background

The paper proves that all prime ideals of every orbit-homomorphism image B_n are completely prime. Since these images provide finite-dimensional approximations to U(W_{a0-1}), the result is presented as evidence for a conjecture concerning the full enveloping algebra.

The conjecture asks whether, for every prime ideal P of U(W_{a0-1}), the quotient U(W_{a0-1})/P is a domain.