Star-polynomial identities: Computing the exponential growth of the codimensions

JOURNAL OF ALGEBRA

卷:469

Article

Giambruno, A.¹  Polcino Milies, C.^2,3  Valenti, A.⁴ 

[1] Univ Palermo, Dipartimento Matemat & Informat, Palermo, Italy

[2] Univ Sao Paulo, Inst Matemat & Estat, Caixa Postal 66281, BR-05315970 Sao Paulo, Brazil

[3] Univ Fed ABC, Av Estados 5001, Santo Andre, SP, Brazil

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

关键词: Polynomial identity;    Involution;    Superinvolution;    Codimensions;   

DOI  :  10.1016/j.jalgebra.2016.07.037

来源: Elsevier

【 摘 要 】

Can one compute the exponential rate of growth of the *-codimensions of a PI-algebra with involution * over a field of characteristic zero? It was shown in [2] that any such algebra A has the same *-identities as the Grassmann envelope of a finite dimensional superalgebra with superinvolution B. Here, by exploiting this result we are able to provide an exact estimate of the exponential rate of growth exp* (A) of any PI-algebra A with involution. It turns out that exp* (A) is an integer and, in case the base field is algebraically closed, it coincides with the dimension of an admissible subalgebra of maximal dimension of B. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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