Surjectivity of the Dixmier map for the one-sided Witt algebra

Prove that the Dixmier map for the one-sided Witt algebra W_{a0-1} is surjective onto the primitive spectrum of U(W_{a0-1}), so that every primitive ideal of U(W_{a0-1}) arises from a Poisson primitive ideal of S(W_{a0-1}).

Background

The paper constructs and studies a Dixmier map from the Poisson primitive spectrum of the symmetric algebra S(W_{a0-1}) to the primitive spectrum of U(W_{a0-1}). It proves that all primitive ideals of the orbit-homomorphism images B_n lie in the image of this map, and establishes further injectivity and inclusion results for one-point local functions.

These results provide evidence for the broader conjecture that every primitive ideal of U(W_{a0-1}) is obtained through the Dixmier construction.