Polynomial codimension growth and the Specht problem

JOURNAL OF ALGEBRA

卷:469

Article

Giambruno, Antonio¹  Mishchenko, Sergey²  Valenti, Angela³  Zaicev, Mikhail⁴ 

[1] Univ Palermo, Dipartimento Matemat & Informat, Via Archirafi 84, I-90123 Palermo, Italy

[2] Ulyanovsk State Univ, Dept Algebra & Geometr Computat, Ulyanovsk 432970, Russia

[3] Univ Palermo, Dipartimento Energia Ingn Informaz & Modelli Mate, I-90128 Palermo, Italy

[4] Moscow MV Lomonosov State Univ, Fac Math & Mech, Dept Algebra, Moscow 119992, Russia

关键词: Polynomial identity;    Codimension;    Growth;   

DOI  :  10.1016/j.jalgebra.2016.09.008

来源: Elsevier

【 摘 要 】

We construct a continuous family of algebras over a field of characteristic zero with slow codimension growth bounded by a polynomial of degree 4. This is achieved by building, for any real number alpha is an element of (0, 1) a commutative nonassociative algebra A(alpha) whose codimension sequence c(n), (A(alpha)), n = 1, 2,..., is polynomially bounded and lim log(n) c(n)(A(alpha)) = 3 + alpha. As an application we are able to construct a new example of a variety with an infinite basis of identities. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free