Abstract
In 2004, Shestakov and Umirbaev proved that the Nagata automorphism of the polynomial algebra in three variables is wild. We fix a [Formula: see text]-grading on this algebra and consider graded-wild automorphisms, i.e. such automorphisms that cannot be decomposed onto elementary automorphisms respecting the grading. We describe all gradings allowing graded-wild automorphisms.
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