{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:LXVY37Q723RITWV2MXVPDJ32AC","short_pith_number":"pith:LXVY37Q7","schema_version":"1.0","canonical_sha256":"5deb8dfe1fd6e289daba65eaf1a77a00b588ae0e9b6df375d90ec479270e0405","source":{"kind":"arxiv","id":"0802.3360","version":1},"attestation_state":"computed","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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0802.3360","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2008-02-22T18:28:39Z","cross_cats_sorted":[],"title_canon_sha256":"bff360c57874e6698700f2a88f6185eee1ebb4a62426aa2f02d15b837ff0e46f","abstract_canon_sha256":"2edad77eefe867d6d29c6230f2d5815446e9dd72bc2eaed27ec76f34493dbc3e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:13.715228Z","signature_b64":"fB+fy3+I226CpS/ryZavy9PNW8TfTGPVZSfONXa5NsZGZPA/ZqXraVeo2tqL9A/lSjDb92Y7uNmxHXN2WYvPBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5deb8dfe1fd6e289daba65eaf1a77a00b588ae0e9b6df375d90ec479270e0405","last_reissued_at":"2026-05-18T04:08:13.714708Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:13.714708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0802.3360","created_at":"2026-05-18T04:08:13.714795+00:00"},{"alias_kind":"arxiv_version","alias_value":"0802.3360v1","created_at":"2026-05-18T04:08:13.714795+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0802.3360","created_at":"2026-05-18T04:08:13.714795+00:00"},{"alias_kind":"pith_short_12","alias_value":"LXVY37Q723RI","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"LXVY37Q723RITWV2","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"LXVY37Q7","created_at":"2026-05-18T12:25:57.157939+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LXVY37Q723RITWV2MXVPDJ32AC","json":"https://pith.science/pith/LXVY37Q723RITWV2MXVPDJ32AC.json","graph_json":"https://pith.science/api/pith-number/LXVY37Q723RITWV2MXVPDJ32AC/graph.json","events_json":"https://pith.science/api/pith-number/LXVY37Q723RITWV2MXVPDJ32AC/events.json","paper":"https://pith.science/paper/LXVY37Q7"},"agent_actions":{"view_html":"https://pith.science/pith/LXVY37Q723RITWV2MXVPDJ32AC","download_json":"https://pith.science/pith/LXVY37Q723RITWV2MXVPDJ32AC.json","view_paper":"https://pith.science/paper/LXVY37Q7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0802.3360&json=true","fetch_graph":"https://pith.science/api/pith-number/LXVY37Q723RITWV2MXVPDJ32AC/graph.json","fetch_events":"https://pith.science/api/pith-number/LXVY37Q723RITWV2MXVPDJ32AC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LXVY37Q723RITWV2MXVPDJ32AC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LXVY37Q723RITWV2MXVPDJ32AC/action/storage_attestation","attest_author":"https://pith.science/pith/LXVY37Q723RITWV2MXVPDJ32AC/action/author_attestation","sign_citation":"https://pith.science/pith/LXVY37Q723RITWV2MXVPDJ32AC/action/citation_signature","submit_replication":"https://pith.science/pith/LXVY37Q723RITWV2MXVPDJ32AC/action/replication_record"}},"created_at":"2026-05-18T04:08:13.714795+00:00","updated_at":"2026-05-18T04:08:13.714795+00:00"}