# Non-abelian extensions of infinite-dimensional Lie groups

@article{Neeb2005NonabelianEO,
title={Non-abelian extensions of infinite-dimensional Lie groups},
author={Karl-Hermann Neeb},
journal={arXiv: Group Theory},
year={2005}
}
• K. Neeb
• Published 2005
• Mathematics
• arXiv: Group Theory
In this paper we study non-abelian extensions of a Lie group $G$ modeled on a locally convex space by a Lie group $N$. The equivalence classes of such extension are grouped into those corresponding to a class of so-called smooth outer actions $S$ of $G$ on $N$. If $S$ is given, we show that the corresponding set $\Ext(G,N)_S$ of extension classes is a principal homogeneous space of the locally smooth cohomology group $H^2_{ss}(G,Z(N))_S$. To each $S$ a locally smooth obstruction class $\chi(S… Expand 32 Citations Lie group extensions associated to projective modules of continuous inverse algebras We call a unital locally convex algebra$A$a continuous inverse algebra if its unit group$A^\times$is open and inversion is a continuous map. For any smooth action of a, possiblyExpand Central Extensions of Lie Groups Preserving a Differential Form • Mathematics • 2019 Let$M$be a manifold with a closed, integral$(k+1)$-form$\omega$, and let$G$be a Fr\'echet-Lie group acting on$(M,\omega)$. As a generalization of the Kostant-Souriau extension for symplecticExpand Quasi-periodic paths and a string 2-group model from the free loop group • Mathematics, Physics • 2017 In this paper we address the question of the existence of a model for the string 2-group as a strict Lie-2-group using the free loop group$LSpin$(or more generally$LG\$ for compact simpleExpand
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