Graded algebras with polynomial growth of their codimensions

JOURNAL OF ALGEBRA

卷:434

Article

Koshlukov, Plamen¹  La Mattina, Daniela² 

[1] Univ Estadual Campinas, Dept Math, BR-13083859 Campinas, SP, Brazil

[2] Univ Palermo, Dipartimento Matemat & Informat, I-90123 Palermo, Italy

关键词: Graded identities;    Graded codimensions;    Codimension growth;    PI exponent;   

DOI  :  10.1016/j.jalgebra.2015.03.030

来源: Elsevier

【 摘 要 】

Let A be an algebra over a field of characteristic 0 and assume A is graded by a finite group G. We study combinatorial and asymptotic properties of the G-graded polynomial identities of A provided A is of polynomial growth of the sequence of its graded codimensions. Roughly speaking this means that the ideal of graded identities is very large. We relate the polynomial growth of the codimensions to the module structure of the multilinear elements in the relatively free G-graded algebra in the variety generated by A. We describe the irreducible modules that can appear in the decomposition, we show that their multiplicities are eventually constant depending on the shape obtained by the corresponding multipartition after removing its first row. We relate, moreover, the polynomial growth to the colengths. Finally we describe in detail the algebras whose graded codimensions are of linear growth. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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