{"paper":{"title":"When does the associated graded Lie algebra of an arrangement group decompose?","license":"","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Alexander I. Suciu, Stefan Papadima","submitted_at":"2003-09-19T14:37:03Z","abstract_excerpt":"Let \\A be a complex hyperplane arrangement, with fundamental group G and holonomy Lie algebra \\H. Suppose \\H_3 is a free abelian group of minimum possible rank, given the values the M\\\"obius function \\mu: \\L_2\\to \\Z takes on the rank 2 flats of \\A. Then the associated graded Lie algebra of G decomposes (in degrees 2 and higher) as a direct product of free Lie algebras. In particular, the ranks of the lower central series quotients of the group are given by \\phi_r(G)=\\sum_{X\\in \\L_2} \\phi_r(F_{\\mu(X)}), for r\\ge 2. We illustrate this new Lower Central Series formula with several families of exa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0309324","kind":"arxiv","version":3},"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"}