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.
${\rm K}_1(\mS_1)$ and the group of automorphisms of the algebra $\mS_2$ of one-sided inverses of a polynomial algebra in two variables
The group of automorphisms of the algebra of one-sided inverses of a polynomial algebra, II
The group of automorphisms of the algebra of one-sided inverses of a polynomial algebra
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