{"paper":{"title":"On the Betti numbers of filiform Lie algebras over fields of characteristic two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Ioannis Tsartsaflis","submitted_at":"2015-11-10T15:14:30Z","abstract_excerpt":"An $n$-dimensional Lie algebra $\\mathfrak{g}$ over a field $\\mathbb{F}$ of characteristic two is said to be of Vergne type if there is a basis $e_1,\\dots,e_n$ such that $[e_1,e_i]=e_{i+1}$ for all $2\\leq i \\leq n-1$ and $[e_i,e_j] = c_{i,j}e_{i+j}$ for some $c_{i,j} \\in \\mathbb{F}$ for all $i,j \\ge 2$ with $i+j \\le n$. We define the algebra $\\mathfrak{m}_0$ by its nontrivial bracket relations: $[e_1,e_i]=e_{i+1}, 2\\leq i \\leq n-1$, and the algebra $\\mathfrak{m}_2$: $[e_1, e_i ]=e_{i+1}, 2 \\le i \\le n-1$, $[e_2, e_j ]=e_{j+2}, 3 \\le j \\le n-2$.\n  We show that, in contrast to the corresponding r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03132","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"}