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Transactions of the American Mathematical Society

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The duality between subsemigroups of Lie groups and monotone functions


Author: Karl-Hermann Neeb
Journal: Trans. Amer. Math. Soc. 329 (1992), 653-677
MSC: Primary 22E15; Secondary 22A15, 26A48
DOI: https://doi.org/10.1090/S0002-9947-1992-1024775-6
MathSciNet review: 1024775
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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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DOI: https://doi.org/10.1090/S0002-9947-1992-1024775-6
Article copyright: © Copyright 1992 American Mathematical Society