{"paper":{"title":"The non-projective part of the Lie module for the symmetric group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Kai Meng Tan, Karin Erdmann","submitted_at":"2010-12-31T13:23:56Z","abstract_excerpt":"The Lie module of the group algebra $FS_n$ of the symmetric group is known to be not projective if and only if the characteristic $p$ of $F$ divides $n$. We show that in this case its non-projective summands belong to the principal block of $FS_n$.\n  Let $V$ be a vector space of dimension $m$ over $F$, and let $L^n(V)$ be the $n$-th homogeneous part of the free Lie algebra on $V$; this is a polynomial representation of $GL_m(F)$ of degree $n$, or equivalently, a module of the Schur algebra $S(m,n)$. Our result implies that, when $m \\geq n$, every summand of $L^n(V)$ which is not a tilting modu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.0254","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"}