FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2013, VOLUME 18, NUMBER 4, PAGES 79-88

**On tame and wild automorphisms of algebras**

C. K. Gupta

V. M. Levchuk

Yu. Yu. Ushakov

Abstract

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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 $Rk/Rk+1$.
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 $Rk$ for every
given integer $k\; >\; 1$.

Location: http://mech.math.msu.su/~fpm/eng/k13/k134/k13406h.htm

Last modified: May 13, 2014