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Fundam. Prikl. Mat., 2013, Volume 18, Issue 4, Pages 79–88 (Mi fpm1530)  

On tame and wild automorphisms of algebras

C. K. Guptaa, V. M. Levchukb, Yu. Yu. Ushakovb

a University of Manitoba, Winnipeg, Canada
b Siberian Federal University, Krasnoyarsk, Russia

Abstract: 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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English version:
Journal of Mathematical Sciences (New York), 2015, 206:6, 660–667

Bibliographic databases:

UDC: 512.552

Citation: C. K. Gupta, V. M. Levchuk, Yu. Yu. Ushakov, “On tame and wild automorphisms of algebras”, Fundam. Prikl. Mat., 18:4 (2013), 79–88; J. Math. Sci., 206:6 (2015), 660–667

Citation in format AMSBIB
\Bibitem{GupLevUsh13}
\by C.~K.~Gupta, V.~M.~Levchuk, Yu.~Yu.~Ushakov
\paper On tame and wild automorphisms of algebras
\jour Fundam. Prikl. Mat.
\yr 2013
\vol 18
\issue 4
\pages 79--88
\mathnet{http://mi.mathnet.ru/fpm1530}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3431833}
\transl
\jour J. Math. Sci.
\yr 2015
\vol 206
\issue 6
\pages 660--667
\crossref{https://doi.org/10.1007/s10958-015-2342-4}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84956834981}


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  • Фундаментальная и прикладная математика
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