Construction of groups associated to Lie- and to Leibniz-algebras
type: Dataset
description: We describe a method for associating to a Lie algebra $\mathfrak{g}$ over a ring $\mathbb{K}$ a sequence of groups $(G_{n}(\mathfrak{g}))_{n\in\mathbb{N}}$, which are {\it polynomial groups} in the sense of Definition \ref{polygroup}. Using a description of these groups by generators and relations, we prove the existence of an action of the symmetric group $\Sigma_{n}$ by automorphisms. The subgroup of fixed points under this action, denoted by $J_{n}(\mathfrak{g})$, is still a polynomial group and we can form the projective limit $J_{\infty}(\mathfrak{g})$ of the sequence $(J_{n}(\mathfrak{g}))_{n\in\mathbb{N}}$. The formal group $J_{\infty}(\mathfrak{g})$ associated in this way to the Lie algebra $\mathfrak{g}$ may be seen as a generalisation of the formal group associated to a Lie algebra over a field of characteristic zero by the Campbell-Haussdorf formula.
issued: 2026-05-07T07:45:34.065800
language: en
modified: 2026-05-07T07:45:34.065804
contact point: Organization
  fn: CCSD
keyword: ams-subject-classification--17b65-14l05
keyword: campbell-haussdorf-formula
keyword: dual-numbers
keyword: exponential-map
keyword: formal-group
keyword: infoeu-reposemanticspreprint
keyword: leibniz-algebra
keyword: lie-algebra
keyword: mathmath-ramathematics-mathrings-and-algebras-mathra
keyword: polynomial-group
keyword: preprints-working-papers-
landing page: https://hal.science/hal-00093436

Construction of groups associated to Lie- and to Leibniz-algebras
type: Distribution
format: HTML
issued: 2026-05-07T07:45:34.067350
modified: 2026-05-07T07:45:34.052121
access URL: https://hal.science/hal-00093436

test_moissonnage_selune
type: Agent