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., 2006, 134(9): 2621–2631]. We prove the sufficiency.

Keywords

Homological epimorphism / complex Lie algebra / Arens–Michael envelope / analytic smash product / relatively quasi-free algebra / 46M18 / 17B30 / 46H05

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