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

Oleg Aristov

doi:10.1007/s11464-024-0114-5

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

Oleg Aristov^*

^*Corresponding author for this work

School of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Journal	Frontiers of Mathematics
DOIs	https://doi.org/10.1007/s11464-024-0114-5
State	Accepted/In press - 2026

Keywords

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

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10.1007/s11464-024-0114-5

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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.",

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KW - analytic smash product

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KW - relatively quasi-free algebra

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

Abstract

Keywords

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