% Encoding: UTF-8
@COMMENT{BibTeX export based on data in FAU CRIS: https://cris.fau.de/}
@COMMENT{For any questions please write to cris-support@fau.de}
@article{faucris.282431288,
abstract = {Let V be a standard subspace in the complex Hilbert space H, and let U : G -> U(H) be a unitary representation of a finite-dimensional Lie group. We assume the existence of an element h is an element of g such that U(exp th) = delta(it)(V) is the modular group of V and that the modular involution J(V) normalizes U(G). We want to determine the semi-group S-V = {g is an element of G: U(g)V subset of V}. In previous work, we have seen that its infinitesimal generators span a Lie algebra on which ad h defines a 3-grading, and here we completely determine the semigroup SV under the assumption that ad h defines a 3-grading on g. Concretely, we show that the ad h-eigenspaces g(+/- 1) contain closed convex cones C-+/- , such that S-V = exp(C+)G(V) exp(C-) , where G(V) = {g is an element of G : U(g)V = V} is the stabilizer of V. To obtain this result, we compare several subsemigroups of G specified by the grading and the positive cone C-U of U. In particular, we show that the orbit O-V = U(G)V with the inclusion order is an ordered symmetric space covering the adjoint orbit O-h = Ad(G)h , endowed with the partial order defined by C-U.},
author = {Neeb, Karl Hermann},
doi = {10.1215/21562261-2022-0017},
faupublication = {yes},
journal = {Kyoto Journal of Mathematics},
note = {CRIS-Team WoS Importer:2022-09-30},
pages = {577-613},
peerreviewed = {Yes},
title = {{Semigroups} in 3-graded {Lie} groups and endomorphisms of standard subspaces},
volume = {62},
year = {2022}
}