Invariant convex sets and functions in Lie algebras |
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Authors: | Karl-Hermann Neeb |
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Affiliation: | 1. Mathematisches Institut, Universit?t Erlangen-Nürnberg, Bismarckstrasse 1 1/2, D-91054, Erlangen, Germany
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Abstract: | We say that an invariant convex coneW in a Lie algebras is elliptic if its interior consists of elliptic elements of . If such a cone exists, then has a compactly embedded Cartan subalgebra. The first main result, of this paper is a characterization of those Lie algebras, which contain elliptic invariant cones. If is an invariant domain in such a cone, then we characterize the invariant locally convex functions onD by their restrictions to where is a compactly embedded Cartan subalgebra. |
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