{"paper":{"title":"On the maximality of the triangular subgroup","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jean-Philippe Furter, Pierre-Marie Poloni","submitted_at":"2016-05-20T13:19:32Z","abstract_excerpt":"We prove that the subgroup of triangular automorphisms of the complex affine $n$-space is maximal among all solvable subgroups of $\\mathrm{Aut}(\\mathbb{A}_{\\mathbb{C}}^n)$ for every $n$. In particular, it is a Borel subgroup of $\\mathrm{Aut}(\\mathbb{A}_{\\mathbb{C}}^n)$, when the latter is viewed as an ind-group. In dimension two, we prove that the triangular subgroup is a maximal closed subgroup. Nevertheless, it is not maximal among all subgroups of $\\mathrm{Aut}(\\mathbb{A}_{\\mathbb{C}}^2)$. Given an automorphism $f$ of $\\mathbb{A}_{\\mathbb{C}}^2$, we study the question whether the group gene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06344","kind":"arxiv","version":2},"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"}