{"paper":{"title":"An abelian quotient of the symplectic derivation Lie algebra of the free Lie algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.QA"],"primary_cat":"math.AT","authors_text":"Masaaki Suzuki, Shigeyuki Morita, Takuya Sakasai","submitted_at":"2016-08-27T01:59:51Z","abstract_excerpt":"We construct an abelian quotient of the symplectic derivation Lie algebra $\\mathfrak{h}_{g,1}$ of the free Lie algebra generated by the fundamental representation of $\\mathrm{Sp}(2g,\\mathbb{Q})$. More specifically, we show that the weight $12$ part of the abelianization of $\\mathfrak{h}_{g,1}$ is $1$-dimensional for $g \\ge 8$. The computation is done with the aid of computers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07645","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"}