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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.
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