{"paper":{"title":"Minimal algebras and $2-$step nilpotent Lie algebras in dimension 7","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AT","authors_text":"Giovanni Bazzoni","submitted_at":"2011-12-01T08:53:04Z","abstract_excerpt":"We use the methods of \\cite{BM} to give a classification of $7-$dimensional minimal algebras, generated in degree 1, over any field $\\bk$ of characteristic $\\textrm{char}(\\bk)\\neq 2$, whose characteristic filtration has length 2. Equivalently, we classify $2-$step nilpotent Lie algebras in dimension 7. This classification also recovers the real homotopy type of $7-$dimensional $2-$step nilmanifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0109","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"}