Invariant orders in simply connected Lie groups.

Gichev, Victor M.

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Invariant orders in Lie groups

Neeb, Karl-Hermann

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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 $G$ 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 $W \subset L (G)$ ...

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Cordero, Luis A., Fernández, Marisa, Gray, Alfred (1990)

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Kamoun, Nouri (1998)

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Globality in semisimple Lie groups

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In the first section of this paper we give a characterization of those closed convex cones (wedges) $W$ in the Lie algebra $s l (2, R)^{n}$ which are invariant under the maximal compact subgroup of the adjoint group and which are controllable in the associated simply connected Lie group $S l (2, R)^{n^{\sim}}$ , i.e., for which the subsemigroup $S = (exp W)$ generated by the exponential image of $W$ agrees with the whole group $G$ (Theorem 13). In Section 2 we develop some algebraic tools concerning real root decompositions with respect to...

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