Invariant orders in Lie groups

Proceedings of the Winter School "Geometry and Physics", GDML_Books, (1991), p. [217]-221 / Harvested from

Résumé

[For the entire collection see Zbl 0742.00067.]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.

MR MR1151908 | Zbl 0755.22003

EUDML-ID : urn:eudml:doc:219983
Mots clés:

@article{701496,
     title = {Invariant orders in Lie groups},
     booktitle = {Proceedings of the Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {1991},
     pages = {[217]-221},
     mrnumber = {MR1151908},
     zbl = {0755.22003},
     url = {http://dml.mathdoc.fr/item/701496}
}

Neeb, Karl-Hermann. Invariant orders in Lie groups, dans Proceedings of the Winter School "Geometry and Physics", GDML_Books,  (1991), pp. [217]-221. http://gdmltest.u-ga.fr/item/701496/