{"paper":{"title":"On a filtration of the second cohomology of nilpotent Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.RA","authors_text":"Dieter Degrijse","submitted_at":"2010-07-29T08:46:40Z","abstract_excerpt":"We study a known filtration of the second cohomology of a finite dimensional nilpotent Lie algebra $\\mathfrak{g}$ with coefficients in a finite dimensional nilpotent $\\mathfrak{g}$-module $M$, that is based upon a refinement of the correspondence between $\\mathrm{H}^2(\\mathfrak{g},M)$ and equivalence classes of abelian extensions of $\\mathfrak{g}$ by $M$. We give a different characterization of this filtration and as a corollary, we obtain an expression for the second Betti number of $\\mathfrak{g}$. Using this expression, we find bounds for the second Betti number and derive a cohomological cr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.5150","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"}