Сибирский федеральный университет

Тип публикации: статья из журнала

Год издания: 2015

Идентификатор DOI: 10.1007/s10958-015-2342-4

Аннотация: Let Bn be a polynomial algebra of n variables over a field F. Considering a free associative algebra An 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 Bn and An. The well-known concept of wild automorphisms of the algebras An and Bn 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. © 2015, Springer Science+Business Media New York.

Журнал: Journal of Mathematical Sciences (United States)

Выпуск журнала: Vol. 206, Is. 6

Номера страниц: 660-667

• Gupta C.K. (Department of Mathematics, University of Manitoba, Winnipeg, Canada)
• Levchuk V.M. (Institute of Mathematics and Computer Science, Siberian Federal University, Krasnoyarsk, Russian Federation)
• Ushakov Y.Y. (Institute of Mathematics and Computer Science, Siberian Federal University, Krasnoyarsk, Russian Federation)

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