Zq-graded identities and central polynomials of the Grassmann algebra

被引：5

作者：

Guimaraes, Alan ^{[1
]}

Fidelis, Claudemir ^{[2
,3
]}

Dias, Laise ^{[2
]}

机构：

[1] Univ Fed Rio Grande do Norte, Dept Matemat, BR-59078970 Natal, RN, Brazil

[2] Univ Fed Campina Grande, Unidade Acad Matemat, BR-58429970 Campina Grande, PB, Brazil

[3] Univ Sao Paulo, Inst Matemat & Estat, BR-05508090 Sao Paulo, SP, Brazil

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2021年 / 609卷

基金：

巴西圣保罗研究基金会;

关键词：

Grassmann algebra; Graded algebra; Graded polynomial; INFINITE-DIMENSIONAL UNITARY; GRADED CENTRAL POLYNOMIALS;

D O I：

10.1016/j.laa.2020.08.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let F be an infinite field of characteristic p different from 2 and let E be the Grassmann algebra generated by an infinite dimensional vector space L over F. In this paper we provide, for any odd prime q, a finite basis for the T-q-ideal of the Z(q) -graded polynomial identities for E and a basis for the T-q space of graded central polynomials for E, for any Z(q)-grading on E such that L is homogeneous in the grading. Moreover, we prove that the set of all graded central polynomials of E is not finitely generated as a T-q-space, if p > 2. In the nonhomogeneous case such bases are also described when at least one non-neutral component has infinite many homogeneous elements of the basis of L in the respective grading. (C) 2020 Elsevier Inc. All rights reserved.

引用

页码：12 / 36

页数：25

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