Journal of Mathematical Sciences

, Volume 206, Issue 6, pp 660–667 | Cite as

On Tame and Wild Automorphisms of Algebras

  • C. K. Gupta
  • V. M. Levchuk
  • Yu. Yu. Ushakov


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.


Tame Chevalley Group Polynomial Algebra Free Associative Algebra Jacobian Conjecture 
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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • C. K. Gupta
    • 1
  • V. M. Levchuk
    • 2
  • Yu. Yu. Ushakov
    • 2
  1. 1.Department of MathematicsUniversity of ManitobaWinnipegCanada
  2. 2.Institute of Mathematics and Computer ScienceSiberian Federal UniversityKrasnoyarskRussia

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