Structure of connected nested automorphism groups
| Autor: | Perepechko, Alexander |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | A nested group is an increasing union of algebraic groups. It is well known that any algebraic subgroup of the automorphism group $\mathrm{Aut}(X)$ of an affine variety $X$ is closed with respect to the ind-topology. The closedness of connected nested subgroups in $\mathrm{Aut}(X)$ is an open question (Kraft--Zaidenberg'2022, arXiv:2203.11356). In this paper, we describe maximal nested unipotent subgroups of $\mathrm{Aut}(X)$ by generalizing the one of triangular automorphisms of $\mathbb{A}^n$. We show that if an abstract subgroup of $\mathrm{Aut}(X)$ consists of unipotent elements, then it is closed if and only if it is nested. This implies that a connected nested subgroup of $\mathrm{Aut}(X)$ is closed. We also extend the recent description of maximal commutative unipotent subgroups (Regeta--van Santen'2024, arXiv:2112.04784), offering a direct construction method and relating them to our description. Comment: 22 pages |
| Databáze: | arXiv |
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