{"paper":{"title":"Membranes and higher groupoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Mikhail Kapranov","submitted_at":"2015-02-22T02:07:10Z","abstract_excerpt":"We study the dg-Lie algebra f_n generated by the coefficients of the universal translation invariant flat dg-connection on the n-dimensional affine space. We describe its \"semiabelianization\" (in particular, the universal quotient which is a crossed module of Lie algebras) in terms of closed differential forms of arbitrary order. This generalizes the theorem of Reutenauer on the abelianization of the commutant of a free Lie algebra.\n  Semiabelian dg-Lie algebras, i.e., non-poisitively graded dg-Lie algebras with brackets of any elements of strictly negative degree being 0, are Lie algebraic an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06166","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"}