{"paper":{"title":"An abstract setting for hamiltonian actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Cornelia Vizman, Karl-Hermann Neeb","submitted_at":"2008-02-22T18:28:39Z","abstract_excerpt":"In this paper we develop an abstract setup for hamiltonian group actions as follows: Starting with a continuous 2-cochain $\\omega$ on a Lie algebra $h$ with values in an $h$-module $V$, we associate subalgebras $sp(h,\\omega) \\supeq ham(h,\\omega)$ of symplectic, resp., hamiltonian elements. Then $ham(h,\\omega)$ has a natural central extension which in turn is contained in a larger abelian extension of $sp(h,\\omega)$. In this setting, we study linear actions of a Lie group $G$ on $V$ which are compatible with a homomorphism $g \\to ham(h,\\omega)$, i.e. abstract hamiltonian actions, corresponding "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.3360","kind":"arxiv","version":1},"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"}