On the maximality of the triangular subgroup
| Autor: | Jean-Philippe Furter, Pierre-Marie Poloni |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Algebra and Number Theory 010102 general mathematics Automorphism 01 natural sciences Mathematics - Algebraic Geometry Mathematics::Group Theory 510 Mathematics 0103 physical sciences FOS: Mathematics 010307 mathematical physics Geometry and Topology Affine transformation 0101 mathematics Algebraic Geometry (math.AG) Mathematics |
| Zdroj: | Furter, Jean-Philippe; Poloni, Pierre-Marie (2018). On the maximality of the triangular subgroup. Annales de l'Institut Fourier, 68(1), pp. 393-421. Association des Annales de l'Institut Fourier 10.5802/aif.3165 |
| DOI: | 10.7892/boris.125528 |
| Popis: | 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 generated by $f$ and the triangular subgroup is equal to the whole group $\mathrm{Aut}(\mathbb{A}_{\mathbb{C}}^2)$. |
| Databáze: | OpenAIRE |
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