{"paper":{"title":"Rota--Baxter operators and post-Lie algebra structures on semisimple Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Dietrich Burde, Vsevolod Gubarev","submitted_at":"2018-05-14T10:57:30Z","abstract_excerpt":"Rota--Baxter operators $R$ of weight $1$ on $\\mathfrak{n}$ are in bijective correspondence to post-Lie algebra structures on pairs $(\\mathfrak{g},\\mathfrak{n})$, where $\\mathfrak{n}$ is complete. We use such Rota--Baxter operators to study the existence and classification of post-Lie algebra structures on pairs of Lie algebras $(\\mathfrak{g},\\mathfrak{n})$, where $\\mathfrak{n}$ is semisimple. We show that for semisimple $\\mathfrak{g}$ and $\\mathfrak{n}$, with $\\mathfrak{g}$ or $\\mathfrak{n}$ simple, the existence of a post-Lie algebra structure on such a pair $(\\mathfrak{g},\\mathfrak{n})$ impl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.05104","kind":"arxiv","version":2},"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"}