Hofmann, Karl H. ; Morris, Sidney A. ; Stroppel, Markus (1996)
Locally compact groups, residual Lie groups, and varieties generated by Lie groups.
In: Topology and its applications, 71 (1)
doi: 10.1016/0166-8641(95)00068-2
Article
Abstract
The concept of approximating in various ways locally compact groups by Lie groups is surveyed with emphasis on pro-Lie groups and locally compact residual Lie groups. All members of the variety of Hausdorff groups generated by the class of all finite dimensional real Lie groups are residual Lie groups. Conversely, we show that every locally compact member of this variety is a pro-Lie group. For every locally compact residual Lie group we construct several better behaved residual Lie groups into which it is equidimensionally immersed. We use such a construction to prove that for a locally compact residual Lie group G the component factor group is residually discrete.
| Item Type: | Article |
|---|---|
| Erschienen: | 1996 |
| Creators: | Hofmann, Karl H. ; Morris, Sidney A. ; Stroppel, Markus |
| Type of entry: | Bibliographie |
| Title: | Locally compact groups, residual Lie groups, and varieties generated by Lie groups |
| Language: | English |
| Date: | 19 June 1996 |
| Publisher: | North-Holland Publicatons |
| Journal or Publication Title: | Topology and its applications |
| Volume of the journal: | 71 |
| Issue Number: | 1 |
| DOI: | 10.1016/0166-8641(95)00068-2 |
| Abstract: | The concept of approximating in various ways locally compact groups by Lie groups is surveyed with emphasis on pro-Lie groups and locally compact residual Lie groups. All members of the variety of Hausdorff groups generated by the class of all finite dimensional real Lie groups are residual Lie groups. Conversely, we show that every locally compact member of this variety is a pro-Lie group. For every locally compact residual Lie group we construct several better behaved residual Lie groups into which it is equidimensionally immersed. We use such a construction to prove that for a locally compact residual Lie group G the component factor group is residually discrete. |
| Divisions: | 04 Department of Mathematics |
| Date Deposited: | 19 Nov 2008 15:59 |
| Last Modified: | 28 Jul 2023 10:55 |
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