{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SMGSJ5SCJ2ZGXULTLIPVYFNRK2","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ea71486c7dc079ee35d18d29aaa982e1e6382954acf8176c8412d6e3585a6e79","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.RA","submitted_at":"2018-06-20T04:56:29Z","title_canon_sha256":"5198a19844ff8261de5aa6434c5d8dbd554a5ee77757340d9368ba205bad6da1"},"schema_version":"1.0","source":{"id":"1806.07553","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.07553","created_at":"2026-05-17T23:56:33Z"},{"alias_kind":"arxiv_version","alias_value":"1806.07553v2","created_at":"2026-05-17T23:56:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07553","created_at":"2026-05-17T23:56:33Z"},{"alias_kind":"pith_short_12","alias_value":"SMGSJ5SCJ2ZG","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SMGSJ5SCJ2ZGXULT","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SMGSJ5SC","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:67c0938debb45d686ab4dd311fe1d9a563421315bea00f99304652287684bf12","target":"graph","created_at":"2026-05-17T23:56:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the coadjoint orbits of a Lie algebra in terms of Cartan class. In fact, the tangent space to a coadjoint orbit $\\mathcal{O}(\\alpha)$ at the point $\\alpha$ corresponds to the characteristic space associated to the left invariant form;$\\alpha$ and its dimension is the even part of the Cartan class of $\\alpha$. We apply this remark to determine Lie algebras such that all the nontrivial orbits (nonreduced to a point) have the same dimension, in particular when this dimension is 2 or 4. We determine also the Lie algebras of dimension $2n$ or $2n+1$ having an orbit of dimension $2n$.","authors_text":"Elisabeth Remm, Michel Goze","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.RA","submitted_at":"2018-06-20T04:56:29Z","title":"Coadjoint orbits of Lie algebras and Cartan class"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07553","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a3ba4f6932786657faa2f64b226980414ffa97bbb63ebb79d5568af34753b249","target":"record","created_at":"2026-05-17T23:56:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ea71486c7dc079ee35d18d29aaa982e1e6382954acf8176c8412d6e3585a6e79","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.RA","submitted_at":"2018-06-20T04:56:29Z","title_canon_sha256":"5198a19844ff8261de5aa6434c5d8dbd554a5ee77757340d9368ba205bad6da1"},"schema_version":"1.0","source":{"id":"1806.07553","kind":"arxiv","version":2}},"canonical_sha256":"930d24f6424eb26bd1735a1f5c15b156802694c79d589b40f371954d429d228d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"930d24f6424eb26bd1735a1f5c15b156802694c79d589b40f371954d429d228d","first_computed_at":"2026-05-17T23:56:33.799566Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:33.799566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vuJDyzF/K3N4z16WngM2kbAOqUd8I+Rnkh3dsgtRvBGJgepC3Ndh6I9BFs8bXZ747gi2GdEruPt6W1ccryxQCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:33.800194Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.07553","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3ba4f6932786657faa2f64b226980414ffa97bbb63ebb79d5568af34753b249","sha256:67c0938debb45d686ab4dd311fe1d9a563421315bea00f99304652287684bf12"],"state_sha256":"b357dd9b4657885b89ccaa149ce31648709b183e6033a690d9aa8cd67e574d1d"}