Automorphisms of polynomial algebras and Dirichlet series

JOURNAL OF ALGEBRA

卷:321

Article

Drensky, Vesselin²  Yu, Jie-Tai¹ 

[1] Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China

[2] Bulgarian Acad Sci, Inst Math & Informat, BU-1113 Sofia, Bulgaria

关键词: Automorphisms;    Polynomial algebras;    Free associative algebras;    Finite fields;    Coordinates;    Nielsen-Schreier varieties;    Dirichlet series;    Generating functions;   

DOI  :  10.1016/j.jalgebra.2008.08.026

来源: Elsevier

【 摘 要 】

Let F-q[x, y] be the polynomial algebra in two variables over the finite field F-q with q elements. We give an exact formula and the asymptotics for the number p of automorphisms (f. g) of F-q[x. y] such that max{deg(f). deg(g)} = n. We describe also the Dirichlet series generating function p(s) = Sigma(n >= 1) pn/n(s) The same results hold for the automorphisms of the free associative algebra F-q (x, y). We have also obtained analogues for free algebras with two generators in Nielsen-Schreier varieties of algebras. (c) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

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