{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:MZTTMHHTLG5PJEOLEBOU4VBOJ2","short_pith_number":"pith:MZTTMHHT","schema_version":"1.0","canonical_sha256":"6667361cf359baf491cb205d4e542e4e882272f6fbd996cb0eb207e22b3311bd","source":{"kind":"arxiv","id":"1705.02631","version":1},"attestation_state":"computed","paper":{"title":"Semi-direct products of Lie algebras and covariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Dmitri Panyushev, Oksana Yakimova","submitted_at":"2017-05-07T15:23:38Z","abstract_excerpt":"The coadjoint representation of a connected algebraic group $Q$ with Lie algebra $\\mathfrak q$ is a thrilling and fascinating object. Symmetric invariants of $\\mathfrak q$ (= $\\mathfrak q$-invariants in the symmetric algebra $S(\\mathfrak q)$) can be considered as a first approximation to the understanding of the coadjoint action $(Q:\\mathfrak q^*)$ and coadjoint orbits. In this article, we study a class of non-reductive Lie algebras, where the description of the symmetric invariants is possible and the coadjoint representation has a number of nice invariant-theoretic properties. If $G$ is a se"},"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":"1705.02631","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-05-07T15:23:38Z","cross_cats_sorted":[],"title_canon_sha256":"d17c6fa6e59d237b2066a38e5007f83f0b2168f045a66e70096c0f4a4960c684","abstract_canon_sha256":"1da01b40d20563047e59d2867ded1bb2ec425920145e646086c1237aae172ea8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:27.592131Z","signature_b64":"Zr9aTDIH2hPTJdTEPrtOBTI68xjTkyxuXP39UMTwGBIflW5ISbx9sKyl0on2ZfeDNs4hAVd5Scr6E65mx6ZpCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6667361cf359baf491cb205d4e542e4e882272f6fbd996cb0eb207e22b3311bd","last_reissued_at":"2026-05-18T00:33:27.591457Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:27.591457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Semi-direct products of Lie algebras and covariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Dmitri Panyushev, Oksana Yakimova","submitted_at":"2017-05-07T15:23:38Z","abstract_excerpt":"The coadjoint representation of a connected algebraic group $Q$ with Lie algebra $\\mathfrak q$ is a thrilling and fascinating object. Symmetric invariants of $\\mathfrak q$ (= $\\mathfrak q$-invariants in the symmetric algebra $S(\\mathfrak q)$) can be considered as a first approximation to the understanding of the coadjoint action $(Q:\\mathfrak q^*)$ and coadjoint orbits. In this article, we study a class of non-reductive Lie algebras, where the description of the symmetric invariants is possible and the coadjoint representation has a number of nice invariant-theoretic properties. If $G$ is a se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02631","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":"1705.02631","created_at":"2026-05-18T00:33:27.591580+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.02631v1","created_at":"2026-05-18T00:33:27.591580+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.02631","created_at":"2026-05-18T00:33:27.591580+00:00"},{"alias_kind":"pith_short_12","alias_value":"MZTTMHHTLG5P","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_16","alias_value":"MZTTMHHTLG5PJEOL","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_8","alias_value":"MZTTMHHT","created_at":"2026-05-18T12:31:31.346846+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/MZTTMHHTLG5PJEOLEBOU4VBOJ2","json":"https://pith.science/pith/MZTTMHHTLG5PJEOLEBOU4VBOJ2.json","graph_json":"https://pith.science/api/pith-number/MZTTMHHTLG5PJEOLEBOU4VBOJ2/graph.json","events_json":"https://pith.science/api/pith-number/MZTTMHHTLG5PJEOLEBOU4VBOJ2/events.json","paper":"https://pith.science/paper/MZTTMHHT"},"agent_actions":{"view_html":"https://pith.science/pith/MZTTMHHTLG5PJEOLEBOU4VBOJ2","download_json":"https://pith.science/pith/MZTTMHHTLG5PJEOLEBOU4VBOJ2.json","view_paper":"https://pith.science/paper/MZTTMHHT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.02631&json=true","fetch_graph":"https://pith.science/api/pith-number/MZTTMHHTLG5PJEOLEBOU4VBOJ2/graph.json","fetch_events":"https://pith.science/api/pith-number/MZTTMHHTLG5PJEOLEBOU4VBOJ2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MZTTMHHTLG5PJEOLEBOU4VBOJ2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MZTTMHHTLG5PJEOLEBOU4VBOJ2/action/storage_attestation","attest_author":"https://pith.science/pith/MZTTMHHTLG5PJEOLEBOU4VBOJ2/action/author_attestation","sign_citation":"https://pith.science/pith/MZTTMHHTLG5PJEOLEBOU4VBOJ2/action/citation_signature","submit_replication":"https://pith.science/pith/MZTTMHHTLG5PJEOLEBOU4VBOJ2/action/replication_record"}},"created_at":"2026-05-18T00:33:27.591580+00:00","updated_at":"2026-05-18T00:33:27.591580+00:00"}