{"paper":{"title":"Cohomology of $\\mathbb{N}$-graded Lie algebras of maximal class over $\\mathbb{Z}_2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Ioannis Tsartsaflis, Yuri Nikolayevsky","submitted_at":"2015-12-24T01:13:15Z","abstract_excerpt":"We compute the cohomology with trivial coefficients of Lie algebras $\\mathfrak{m}_0$ and $\\mathfrak{m}_2$ of maximal class over the field $\\mathbb{Z}_2$. In the infinite-dimensional case, we show that the cohomology rings $H^*(\\mathfrak{m}_0)$ and $H^*(\\mathfrak{m}_2)$ are isomorphic, in contrast with the case of the ground field of characteristic zero, and we obtain a complete description of them. In the finite-dimensional case, we find the first three Betti numbers of $\\mathfrak{m}_0(n)$ and $\\mathfrak{m}_2(n)$ over $\\mathbb{Z}_2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07676","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"}