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[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 admits a continuous invariant order if and only if its Lie algebra contains a pointed invariant cone. V. M. Gichev has proved this theorem for solvable simply connected Lie groups (1989). If is solvable and simply connected then all pointed invariant cones in are global in (a Lie wedge is said to be global in if for a Lie semigroup ). This is false in general if is a simple simply connected Lie group.
Neeb, Karl-Hermann. "Invariant orders in Lie groups." Proceedings of the Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 1991. [217]-221. <http://eudml.org/doc/219983>.
@inProceedings{Neeb1991, abstract = {[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.}, author = {Neeb, Karl-Hermann}, booktitle = {Proceedings of the Winter School "Geometry and Physics"}, keywords = {Srni (Czechoslovakia); Proceedings; Winter school; Geometry; Physics}, location = {Palermo}, pages = {[217]-221}, publisher = {Circolo Matematico di Palermo}, title = {Invariant orders in Lie groups}, url = {http://eudml.org/doc/219983}, year = {1991}, }
TY - CLSWK AU - Neeb, Karl-Hermann TI - Invariant orders in Lie groups T2 - Proceedings of the Winter School "Geometry and Physics" PY - 1991 CY - Palermo PB - Circolo Matematico di Palermo SP - [217] EP - 221 AB - [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. KW - Srni (Czechoslovakia); Proceedings; Winter school; Geometry; Physics UR - http://eudml.org/doc/219983 ER -