{"paper":{"title":"Outer automorphisms of adjoint groups of type D and non-rational adjoint groups of outer type A","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Demba Barry, Jean-Pierre Tignol","submitted_at":"2018-07-02T08:48:58Z","abstract_excerpt":"For a classical group $G$ of type $\\mathsf D_n$ over a field $k$ of characteristic different from $2$, we show the existence of a finitely generated regular extension $R$ of $k$ such that $G$ admits outer automorphisms over $R$. Using this result and a construction of groups of type $\\mathsf A$ from groups of type $\\mathsf D$, we construct new examples of groups of type $^2\\mathsf A_n$ with $n\\equiv 3\\bmod 4$ and the first examples of type $^2\\mathsf A_n$ with $n\\equiv 1\\bmod 4$ $(n\\geq 5)$ that are not $R$-trivial, hence not rational (nor stably rational)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00535","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"}