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

Abstract

The Arens-Michael envelope of the universal enveloping algebra of a finite-dimensional complex Lie algebra is a homological epimorphism if and only if the Lie algebra is solvable. The necessity was proved by Pirkovskii in [Proc. Amer. Math. Soc. 134, 2621--2631, 2006]. We prove the sufficiency.

V.7 minor changes, V.5. new proof of Pr.3.2, V.3: L.4.3 became Th.11, V.2: Th. 4.6 is given in a general form + minor corrections