2012/09/30 by Immanuel Stampfli · 1 citation
Mathematics · #Advanced Differential Equations and Dynamical Systems #Affine transformation #Algebraic Geometry and Number Theory #Automorphism #Automorphism group #Combinatorics #Dimension (graph theory) #Geometry #Group (periodic table) #Mathematics #Meromorphic and Entire Functions #Physics #Pure mathematics #Torus #Unipotent #math.AC #math.AG
paper · pdf · doi:10.4310/mrl.2013.v20.n6.a14
published as Mathematical Research Letters, 20 no. 6 (2013), p. 1177-1181 · 5 pages, typos corrected, minor changes, improved exposition
openalex publication_date 2013/01/01 · arxiv created 2016/11/23 · arxiv updated 2016/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Let G be an ind-group and let U G be a unipotent ind-subgroup. We prove that an abstract group automorphism : G G maps U isomorphically onto a unipotent ind-subgroup of G, provided that fixes a closed torus T G, which normalizes U and the action of T on 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 Cremona group G 3 in dimension 3 fixes the subgroup of tame automorphisms T G 3 , then it also fixes a whole family of non-tame automorphisms (including the Nagata automorphism).