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<p>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.</p>

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The Arens–Michael Envelope of a Solvable Lie Algebra is a Homological Epimorphism

  • 期刊论文

  • 发表日期：

    2026年4月30日

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  • Oleg Aristov

摘要

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.