Non-abelian extensions of infinite-dimensional Lie groups
| dc.creator | Neeb, Karl-Hermann | |
| dc.date | 2005-04-14 | |
| dc.date.accessioned | 2026-07-07T05:19:07Z | |
| dc.date.available | 2026-07-07T05:19:07Z | |
| dc.description | 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 $χ(S)$ in a suitably defined cohomology group $H^3_{ss}(G,Z(N))_S$ is defined. It vanishes if and only if there is a corresponding extension of $G$ by $N$. A central point is that we reduce many problems concerning extensions by non-abelian groups to questions on extensions by abelian groups, which have been dealt with in previous work. An important tool is a Lie theoretic concept of a smooth crossed module $α: H \to G$, which we view as a central extension of a normal subgroup of $G$. | |
| dc.identifier | https://arxiv.org/abs/math/0504295 | |
| dc.identifier | http://arxiv.org/abs/math/0504295 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74900 | |
| dc.subject | Group Theory | |
| dc.subject | 22E65, 57T10, 22E15 | |
| dc.title | Non-abelian extensions of infinite-dimensional Lie groups | |
| dc.type | text |