The duality between subsemigroups of Lie groups and monotone functions

Neeb, Karl-Hermann

doi:10.1090/S0002-9947-1992-1024775-6

The duality between subsemigroups of Lie groups and monotone functions
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by Karl-Hermann Neeb PDF

Trans. Amer. Math. Soc. 329 (1992), 653-677 Request permission

Abstract:

In this paper we give a characterization of those convex cones $W$ in the Lie algebra ${\mathbf {L}}(G)$ of a connected Lie group $G$ which are global in $G$, i.e. for which there exists a closed subsemigroup $S$ in $G$ having $W$ as its tangent wedge ${\mathbf {L}}(S)$. The main result is the Characterization Theorem II.12. We also prove in Corollary II.6 that each germ of a strictly $W$-positive function belongs to a global function if there exists at least one strictly $W$-positive function. We apply the Characterization Theorem to obtain some general conditions for globality and to give a complete description of the global cones in compact Lie algebras.

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Invariant orderings in simple Lie groups. The solution to E. B. Vinberg’s problem

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