{"paper":{"title":"A note on Automorphisms of the Affine Cremona Group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Immanuel Stampfli","submitted_at":"2012-09-15T18:39:46Z","abstract_excerpt":"Let $\\mathcal{G}$ be an ind-group and let $\\mathcal{U} \\subseteq \\mathcal{G}$ be a unipotent ind-subgroup. We prove that an abstract group automorphism $\\theta \\colon \\mathcal{G} \\to \\mathcal{G}$ maps $\\mathcal{U}$ isomorphically onto a unipotent ind-subgroup of $\\mathcal{G}$, provided that $\\theta$ fixes a closed torus $T \\subseteq \\mathcal{G}$, which normalizes $\\mathcal{U}$ and the action of $T$ on $\\mathcal{U}$ by conjugation fixes only the neutral element. As an application we generalize a result by Hanspeter Kraft and the author as follows: If an abstract group automorphism of the affine"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3427","kind":"arxiv","version":3},"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"}