{"paper":{"title":"Lower central series of free algebras in symmetric tensor categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RT"],"primary_cat":"math.RA","authors_text":"Asilata Bapat, David Jordan","submitted_at":"2010-01-08T22:51:12Z","abstract_excerpt":"We continue the study of the lower central series of a free associative algebra, initiated by B. Feigin and B. Shoikhet (arXiv:math/0610410). We generalize via Schur functors the constructions of the lower central series to any symmetric tensor category; specifically we compute the modified first quotient \\bar{B}_1, and second and third quotients B_2, and B_3 of the series for a free algebra T(V) in any symmetric tensor category, generalizing the main results of (arXiv:math/0610410) and (arXiv:0902.4899). In the case A_{m|n}:=T(\\CC^{m|n}), we use these results to compute the explicit Hilbert s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.1375","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"}