{"paper":{"title":"On extensions for Ree groups of type F_4","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"David I. Stewart","submitted_at":"2013-04-09T11:53:20Z","abstract_excerpt":"Let k be an algebraically closed field of characteristic p=2. Let G=F_4 be simply connected over k and let \\sigma:G\\to G be an endomorphism such that the fixed point set G(\\sigma) is a Ree group. We show, using the methods of Bendel--Nakano--Pillen, that self-extensions of simple kG(\\sigma)-modules vanish generically and that for all but the first few Ree groups of type F_4, the 1-cohomology for G(\\sigma) with coefficients in simple kG-modules can be identified with the 1-cohomology for G with coefficients in (possibly different) simple G-modules."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2544","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"}