{"paper":{"title":"Some non-Koszul algebras from rational homotopy theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.RA","authors_text":"Andrew Conner, Peter Goetz","submitted_at":"2014-07-17T16:18:51Z","abstract_excerpt":"The McCool group, denoted $P\\Sigma_n$, is the group of pure symmetric automorphisms of a free group of rank $n$. The cohomology algebra $H^*(P\\Sigma_n, \\mathbb{Q})$ was determined by Jensen, McCammond and Meier. We prove that $H^*(P\\Sigma_n, \\mathbb{Q})$ is a non-Koszul algebra for $n \\geq 4$, which answers a question of Cohen and Pruidze. We also study the enveloping algebra of the graded Lie algebra associated to the lower central series of $P\\Sigma_n$, and prove that it has two natural decompositions as a smash product of algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4726","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"}