Fundamentals of direct limit Lie theory
| dc.creator | Glockner, Helge | |
| dc.date | 2004-03-04 | |
| dc.date | 2004-05-14 | |
| dc.date.accessioned | 2026-07-07T05:06:07Z | |
| dc.date.available | 2026-07-07T05:06:07Z | |
| dc.description | We show that every countable direct system of finite-dimensional real or complex Lie groups has a direct limit in the category of Lie groups modelled on locally convex spaces. This enables us to push all basic constructions of finite-dimensional Lie theory to the case of direct limit groups. In particular, we obtain an analogue of Lie's third theorem: Every countable-dimensional real or complex locally finite Lie algebra is enlargible, i.e., it is the Lie algebra of some regular Lie group (a suitable direct limit group). | |
| dc.description | 33 pages (v2: Lemma 7.12 and Proposition 7.13 corrected, clearer distinction between analyticity and convenient analyticity) | |
| dc.identifier | https://arxiv.org/abs/math/0403093 | |
| dc.identifier | http://arxiv.org/abs/math/0403093 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70361 | |
| dc.subject | Group Theory | |
| dc.subject | 22E65 (Primary) 46T05, 57N40, 58B10, 58B25 (Secondary) | |
| dc.title | Fundamentals of direct limit Lie theory | |
| dc.type | text |