{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:2OQIILBS57E5KTHZG75TCJQM43","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":"d27d18ba29b00b515f5c7085cb7739c65e27788068176533d99a22f9b4d7c33a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-06-24T11:24:43Z","title_canon_sha256":"fa17b1ec70ddedcc29f5742f05fc403536462a0bc2c8e803f7cb3c39d70aca20"},"schema_version":"1.0","source":{"id":"1906.09854","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.09854","created_at":"2026-05-17T23:42:36Z"},{"alias_kind":"arxiv_version","alias_value":"1906.09854v1","created_at":"2026-05-17T23:42:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.09854","created_at":"2026-05-17T23:42:36Z"},{"alias_kind":"pith_short_12","alias_value":"2OQIILBS57E5","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"2OQIILBS57E5KTHZ","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"2OQIILBS","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:b736adb25f05e1f60bdfd0d884eb794a0bcd2dfaf4c0a4f35eed925ca7a8e9b9","target":"graph","created_at":"2026-05-17T23:42:36Z","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 introduce post-associative algebra structures and study their relationship to post-Lie algebra structures, Rota--Baxter operators and decompositions of associative algebras and Lie algebras. We show several results on the existence of such structures. In particular we prove that there exists no post-Lie algebra structure on a pair $(\\mathfrak{g},\\mathfrak{n})$, where $\\mathfrak{n}$ is a simple Lie algebra and $\\mathfrak{g}$ is a reductive Lie algebra, which is not isomorphic to $\\mathfrak{n}$. We also show that there is no post-associative algebra structure on a pair $(A,B)$ arising from a ","authors_text":"Dietrich Burde, Vsevolod Gubarev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-06-24T11:24:43Z","title":"Decompositions of algebras and post-associative algebra structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09854","kind":"arxiv","version":1},"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":"sha256:2455871978ef85fd576a83dfdca2cb48f50d5966dedb935bffd6ed7c9d039e34","target":"record","created_at":"2026-05-17T23:42:36Z","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":"d27d18ba29b00b515f5c7085cb7739c65e27788068176533d99a22f9b4d7c33a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-06-24T11:24:43Z","title_canon_sha256":"fa17b1ec70ddedcc29f5742f05fc403536462a0bc2c8e803f7cb3c39d70aca20"},"schema_version":"1.0","source":{"id":"1906.09854","kind":"arxiv","version":1}},"canonical_sha256":"d3a0842c32efc9d54cf937fb31260ce6ec499b181c610f8c34846651b60231e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3a0842c32efc9d54cf937fb31260ce6ec499b181c610f8c34846651b60231e6","first_computed_at":"2026-05-17T23:42:36.459884Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:36.459884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZPUpze9kfcDWxLJnHcwxNL+87Q3+3pkWVK8Q090Cpm4XhVYM2UIxvVLuRHLAq1ihEtjj9TJV9YdyNujDc9s1Aw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:36.460602Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.09854","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2455871978ef85fd576a83dfdca2cb48f50d5966dedb935bffd6ed7c9d039e34","sha256:b736adb25f05e1f60bdfd0d884eb794a0bcd2dfaf4c0a4f35eed925ca7a8e9b9"],"state_sha256":"818eead31b93aea306f25a01c732a029691ba500a92856c509fb136f1d42f35c"}