{"paper":{"title":"Semigroups in 3-graded Lie groups and endomorphisms of standard subspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA","math.RT"],"primary_cat":"math.FA","authors_text":"Karl-Hermann Neeb","submitted_at":"2019-12-31T15:54:54Z","abstract_excerpt":"Let V be a standard subspace in the complex Hilbert space H and U : G \\to U(H) be a unitary representation of a finite dimensional Lie group. We assume the existence of an element h in the Lie algebra of G such that U(exp th) is the modular group of V and that the modular involution J_V normalizes U(G). We want to determine the semigroup $S_V = \\{ g\\in G : U(g)V \\subseteq V\\}.$ 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 S_V under the assumption that ad h defines a 3-grading"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.13367","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/1912.13367/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"}