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arXiv · 1011.3349

On the lifting of the Nagata automorphism

Alexei Belov-Kanel·Jie-Tai Yu
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Abstract

It is proved that the Nagata automorphism (Nagata coordinates, respectively) of the polynomial algebra $F[x,y,z]$ over a field $F$ cannot be lifted to a $z$-automorphism ($z$-coordinate, respectively) of the free associative algebra $K $. The proof is based on the following two new results which have their own interests: degree estimate of ${Q*_FF }$ and tameness of the automorphism group ${\text{Aut}_Q(Q*_FF )}$.

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Alexei Belov-Kanel, Jie-Tai Yu. 2010-11-15. On the lifting of the Nagata automorphism. https://doi.org/10.1007/s00029-011-0061-3

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