{"paper":{"title":"Post-Lie algebra structures for nilpotent Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Christof Ender, Dietrich Burde, Wolfgang Alexander Moens","submitted_at":"2018-01-17T13:24:37Z","abstract_excerpt":"We study post-Lie algebra structures on $(\\mathfrak{g},\\mathfrak{n})$ for nilpotent Lie algebras. First we show that if $\\mathfrak{g}$ is nilpotent such that $H^0(\\mathfrak{g},\\mathfrak{n})=0$, then also $\\mathfrak{n}$ must be nilpotent, of bounded class. For post-Lie algebra structures $x\\cdot y$ on pairs of $2$-step nilpotent Lie algebras $(\\mathfrak{g},\\mathfrak{n})$ we give necessary and sufficient conditions such that $x\\circ y=\\frac{1}{2}(x\\cdot y+y\\cdot x)$ defines a CPA-structure on $\\mathfrak{g}$, or on $\\mathfrak{n}$. As a corollary we obtain that every LR-structure on a Heisenberg L"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.05652","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"}