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    On the lifting of the Nagata automorphism

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    It is proved that the Nagata automorphism (Nagata coordinates, respectively) of the polynomial algebra F[x,y,z]F[x,y,z] over a field FF cannot be lifted to a zz-automorphism (zz-coordinate, respectively) of the free associative algebra KK. The proof is based on the following two new results which have their own interests: degree estimate of Q∗FF{Q*_FF} and tameness of the automorphism group AutQ(Q∗FF){\text{Aut}_Q(Q*_FF)}.Comment: 15 page
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