On the lifting of the Nagata automorphism

Details On the lifting of the Nagata automorphism On the lifting of the Nagata automorphism

2010-11-15

arxiv.org/abs/1011.3349v4

Mathematics

Commutative Algebra

15 pages

Scientific paper

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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