The Arens-Michael envelope of a nilpotent Lie algebra is a homological epimorphism

In his pioneering work, Joseph Taylor observed that the Arens-Michael envelope of the universal enveloping algebra of a complex Lie algebra is a homological epimorphism in the abelian case and is not a homological epimorphism in the semisimple case. On the other hand, Pirkovskii proved that the solvability of the Lie algebra is a necessary condition. Sufficient conditions for nilpotent Lie algebras were obtained by Pirkovskii and Dosiev. We will prove the conjecture for an arbitrary nilpotent Lie algebra. The proof involves (quite unexpectedly) such notions as the growth of an entire function and the Riemannian metric.