Geodesic
On tame and wild automorphisms of algebras
Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 4, pp. 79-88

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Let $B_n$ be a polynomial algebra of $n$ variables over a field $F$. Considering a free associative algebra $A_n$ of rank $n$ over $F$ as a polynomial algebra of noncommuting variables, we choose the ideal $R$ of all polynomials with a zero absolute term in $B_n$ and $A_n$. The well-known concept of wild automorphisms of the algebras $A_n$ and $B_n$ is transferred to $R$; the study of wild automorphisms is reduced to monic automorphisms of the algebra $R$, i.e., those identical on each factor $R^k/R^{k+1}$. In particular, this enables us to study the properties of the known Nagata and Anik automorphisms in detail. For $n=3$ we investigate the hypothesis that the Anik automorphism is tame modulo $R^k$ for every given integer $k>1$. 
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     author = {C. K. Gupta and V. M. Levchuk and Yu. Yu. Ushakov},
     title = {On tame and wild automorphisms of algebras},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
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     number = {4},
     year = {2013},
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C. K. Gupta; V. M. Levchuk; Yu. Yu. Ushakov. On tame and wild automorphisms of algebras. Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 4, pp. 79-88. http://geodesic.mathdoc.fr/item/FPM_2013_18_4_a5/