Lie groups of bundle automorphisms and their extensions
| dc.creator | Neeb, Karl-Hermann | |
| dc.date | 2007-09-07 | |
| dc.date.accessioned | 2026-07-07T08:28:10Z | |
| dc.date.available | 2026-07-07T08:28:10Z | |
| dc.description | We describe natural abelian extensions of the Lie algebra $\aut(P)$ of infinitesimal automorphisms of a principal bundle over a compact manifold $M$ and discuss their integrability to corresponding Lie group extensions. Already the case of a trivial bundle $P = M \times K$ is quite interesting. In this case, we show that essentially all central extensions of the gauge algebra $C^\infty(M,\fk)$ can be obtained from three fundamental types of cocycles with values in one of the spaces $\fz := C^\infty(M,V)$, $Ω^1(M,V)$ and $Ω^1(M,V)/\dd C^\infty(M,V)$. These cocycles extend to $\aut(P)$, and, under the assumption that $TM$ is trivial, we also describe the space $H^2({\cal V}(M),\fz)$ classifying the twists of these extensions. We then show that all fundamental types have natural generalizations to non-trivial bundles and explain under which conditions they extend to $\aut(P)$ and integrate to global Lie group extensions. | |
| dc.identifier | https://arxiv.org/abs/0709.1063 | |
| dc.identifier | http://arxiv.org/abs/0709.1063 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/137523 | |
| dc.subject | Differential Geometry | |
| dc.subject | 22E65; 22E67;17B66 | |
| dc.title | Lie groups of bundle automorphisms and their extensions | |
| dc.type | text |