A formal Lie correspondence

Fuente: arXiv
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Main Author: Bagayoko, Vincent
Format: Preprint
Published: 2026
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author Bagayoko, Vincent
author_facet Bagayoko, Vincent
contents We establish an equivalence between categories of 'formally nilpotent' Lie algebras and exponential groups in characteristic zero. It extends the equivalences of Mal'cev, Lazard, Quillen and Warfield, and applies to groups under composition of generalized formal series or automorphisms of algebras of generalized formal series. We obtain first-order transfer results from finite dimensional nilpotent objects to formally nilpotent ones. We give applications to solving equations over groups, to the theory of nilpotent exponential groups as per Miasnikov-Remeslennikov, and to definability problems in certain groups of formal series.
format Preprint
id arxiv_https___arxiv_org_abs_2604_04224
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle A formal Lie correspondence
Bagayoko, Vincent
Rings and Algebras
Group Theory
Logic
We establish an equivalence between categories of 'formally nilpotent' Lie algebras and exponential groups in characteristic zero. It extends the equivalences of Mal'cev, Lazard, Quillen and Warfield, and applies to groups under composition of generalized formal series or automorphisms of algebras of generalized formal series. We obtain first-order transfer results from finite dimensional nilpotent objects to formally nilpotent ones. We give applications to solving equations over groups, to the theory of nilpotent exponential groups as per Miasnikov-Remeslennikov, and to definability problems in certain groups of formal series.
title A formal Lie correspondence
topic Rings and Algebras
Group Theory
Logic
url https://arxiv.org/abs/2604.04224