{"paper":{"title":"Nets of standard subspaces on Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.OA","math.RT"],"primary_cat":"math-ph","authors_text":"Gestur Olafsson, Karl-Hermann Neeb","submitted_at":"2020-06-16T14:59:35Z","abstract_excerpt":"Let G be a Lie group with Lie algebra $\\mathfrak{g}$, $h \\in \\frak{g}$ an element for which the derivation ad(h) defines a 3-grading of $\\mathfrak{g}$ and $\\tau_G$ an involutive automorphism of G inducing on $\\mathfrak{g}$ the involution $e^{\\pi i ad(h)}$. We consider antiunitary representations $U$ of the Lie group $G_\\tau = G \\rtimes \\{e,\\tau_G\\}$ for which the positive cone $C_U = \\{ x \\in \\mathfrak{g} : -i \\partial U(x) \\geq 0\\}$ and $h$ span $\\mathfrak{g}$. To a real subspace E of distribution vectors invariant under $exp(\\mathbb{R} h)$ and an open subset $O \\subseteq G$, we associate the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.09832","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2006.09832/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}