| Title:
|
Invariant orders in Lie groups (English) |
| Author:
|
Neeb, Karl-Hermann |
| Language:
|
English |
| Journal:
|
Proceedings of the Winter School "Geometry and Physics" |
| Volume:
|
|
| Issue:
|
1990 |
| Year:
|
|
| Pages:
|
[217]-221 |
| . |
| Category:
|
math |
| . |
| Summary:
|
[For the entire collection see Zbl 0742.00067.]\par The author formulates several theorems about invariant orders in Lie groups (without proofs). The main theorem: a simply connected Lie group $G$ admits a continuous invariant order if and only if its Lie algebra $L(G)$ contains a pointed invariant cone. V. M. Gichev has proved this theorem for solvable simply connected Lie groups (1989). If $G$ is solvable and simply connected then all pointed invariant cones $W$ in $L(G)$ are global in $G$ (a Lie wedge $W\subset L(G)$ is said to be global in $G$ if $W=L(S)$ for a Lie semigroup $S\subset G$). This is false in general if $G$ is a simple simply connected Lie group. (English) |
| MSC:
|
17B05 |
| MSC:
|
22A15 |
| MSC:
|
22E15 |
| MSC:
|
54F05 |
| idZBL:
|
Zbl 0755.22003 |
| idMR:
|
MR1151908 |
| . |
| Date available:
|
2009-07-13T21:27:53Z |
| Last updated:
|
2012-09-18 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/701496 |
| . |
