| Title | Linearity and nonlinearity of groups of polynomial automorphisms of the plane |
| Author | |
| Corresponding Author | Mathieu, Olivier |
| Publication Years | 2024
|
| DOI | |
| Source Title | |
| ISSN | 0021-8693
|
| EISSN | 1090-266X
|
| Volume | 637 |
| Abstract | Given a field K, we investigate which subgroups of the group Aut A2K of polynomial automorphisms of the plane are linear or not. The results are contrasted. The group Aut A2K itself is nonlinear, except if K is finite, but it contains some large subgroups, of "codimension-five" or more, which are linear. This phenomenon is specific to dimension two: it is easy to prove that any natural "finite-codimensional" subgroup of Aut A3K is nonlinear, even for a finite field K. When ch K = 0, we also look at a similar questions for f.g. subgroups, and the results are again disparate. The group Aut A2K has a one-related f.g. subgroup which is not linear. However, there is a large subgroup, of "codimension-three", which is locally linear but not linear.(c) 2023 Elsevier Inc. All rights reserved. |
| Keywords | |
| URL | [Source Record] |
| Indexed By | |
| Language | English
|
| SUSTech Authorship | Corresponding
|
| WOS Research Area | Mathematics
|
| WOS Subject | Mathematics
|
| WOS Accession No | WOS:001087036700001
|
| Publisher | |
| ESI Research Field | MATHEMATICS
|
| Data Source | Web of Science
|
| Citation statistics | |
| Document Type | Journal Article |
| Identifier | http://kc.sustech.edu.cn/handle/2SGJ60CL/582845 |
| Affiliation | 1.UCBL, CNRS, Inst Camille Jordan, F-69622 Villeurbanne, France 2.SUSTech, Shenzhen Int Ctr Math, Shenzhen, Peoples R China |
| First Author Affilication | Southern University of Science and Technology |
| Corresponding Author Affilication | Southern University of Science and Technology |
| Recommended Citation GB/T 7714 |
Mathieu, Olivier. Linearity and nonlinearity of groups of polynomial automorphisms of the plane[J]. JOURNAL OF ALGEBRA,2024,637.
|
| APA |
Mathieu, Olivier.(2024).Linearity and nonlinearity of groups of polynomial automorphisms of the plane.JOURNAL OF ALGEBRA,637.
|
| MLA |
Mathieu, Olivier."Linearity and nonlinearity of groups of polynomial automorphisms of the plane".JOURNAL OF ALGEBRA 637(2024).
|
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