Gradings allowing wild automorphisms

In 2004 Shestakov and Umirbaev proved that the Nagata automorphism of the polynomial algebra in three variables is wild. We fix a Z-grading on this algebra and consider graded-wild automorphisms, i.e. such automorphisms that can not be decomposed onto elementary automorphisms respecting the grading....

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Bibliographic Details
Published inarXiv.org
Main Author Trushin, Anton
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 08.04.2021
Subjects
Automorphisms
Mathematical analysis
Polynomials
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Summary:In 2004 Shestakov and Umirbaev proved that the Nagata automorphism of the polynomial algebra in three variables is wild. We fix a Z-grading on this algebra and consider graded-wild automorphisms, i.e. such automorphisms that can not be decomposed onto elementary automorphisms respecting the grading. We describe all gradings allowing graded-wild automorphisms.
ISSN:2331-8422