Lie group extensions associated to projective modules of continuous inverse algebras
| dc.creator | Neeb, Karl-Hermann | |
| dc.date | 2008-02-21 | |
| dc.date.accessioned | 2026-07-07T09:22:16Z | |
| dc.date.available | 2026-07-07T09:22:16Z | |
| dc.description | 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, possibly infinite-dimensional, connected Lie group $G$ on a continuous inverse algebra $A$ by automorphisms and any finitely generated projective right $A$-module $E$, we construct a Lie group extension $\hat G$ of $G$ by the group $\GL_A(E)$ of automorphisms of the $A$-module $E$. This Lie group extension is a ``non-commutative'' version of the group $\Aut(\V)$ of automorphism of a vector bundle over a compact manifold $M$, which arises for $G = \Diff(M)$, $A = C^\infty(M,\C)$ and $E = Γ\V$. We also identify the Lie algebra $\hat\g$ of $\hat G$ and explain how it is related to connections of the $A$-module $E$. | |
| dc.identifier | https://arxiv.org/abs/0802.2993 | |
| dc.identifier | http://arxiv.org/abs/0802.2993 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155315 | |
| dc.subject | Operator Algebras | |
| dc.subject | Rings and Algebras | |
| dc.subject | 22E65, 58B34 | |
| dc.title | Lie group extensions associated to projective modules of continuous inverse algebras | |
| dc.type | text |