{"paper":{"title":"On unipotent algebraic G-groups and 1-cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA","math.RT"],"primary_cat":"math.GR","authors_text":"David I. Stewart","submitted_at":"2010-11-04T15:09:34Z","abstract_excerpt":"In this paper we consider non-abelian 1-cohomology for groups with coefficients in other groups. We prove versions of the `five lemma' arising from this situation. We go on to show that a connected unipotent algebraic group Q acted on morphically by a connected algebraic group G admits a filtration with successive quotients having the structure of G-modules. From these results we deduce extensions to results due to Cline, Parshall, Scott and van der Kallen. Firstly, if G is a connected, reductive algebraic group with Borel subgroup B and Q a unipotent algebraic G-group, we show the restriction"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1183","kind":"arxiv","version":6},"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"}