{"paper":{"title":"Representations of Lie Algebras by non-Skewselfadjoint Operators in Hilbert Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.DS","authors_text":"Eli Shamovich, Victor Vinnikov","submitted_at":"2012-09-19T12:28:10Z","abstract_excerpt":"We study non-selfadjoint representations of a finite dimensional real Lie algebra $\\fg$. To this end we embed a non-selfadjoint representation of $\\fg$ into a more complicated structure, that we call a $\\fg$-operator vessel and that is associated to an overdetermined linear conservative input/state/output system on the corresponding simply connected Lie group $\\fG$. We develop the frequency domain theory of the system in terms of representations of $\\fG$, and introduce the joint characteristic function of a $\\fg$-operator vessel which is the analogue of the classical notion of the characterist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4224","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}