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@article{faucris.267814545,
abstract = {In this note, we study in a finite dimensional Lie algebra g the set of all those elements x for which the closed convex hull of the adjoint orbit contains no affine lines; this contains in particular elements whose adjoint orbits generates a pointed convex cone C-x. Assuming that g is admissible, i.e., contains a generating invariant convex subset not containing affine lines, we obtain a natural characterization of such elements, also for non-reductive Lie algebras. Motivated by the concept of standard (Borchers) pairs in QFT, we also study pairs (x, h) of Lie algebra elements satisfying [h, x] = x for which Cx pointed. Given x, we show that such elements h can be constructed in such a way that ad h defines a 5-grading, and characterize the cases where we even get a 3-grading.},
author = {Neeb, Karl-Hermann and Oeh, Daniel},
doi = {10.1007/s41980-021-00671-y},
faupublication = {yes},
journal = {Bulletin of the Iranian Mathematical Society},
note = {CRIS-Team WoS Importer:2022-01-07},
peerreviewed = {Yes},
title = {{Elements} in {Pointed} {Invariant} {Cones} in {Lie} {Algebras} and {Corresponding} {Affine} {Pairs}},
year = {2021}
}