THE CENTRAL POLYNOMIALS FOR THE GRASSMANN ALGEBRA

被引：19

作者：

Brandao, Antonio Pereira, Jr. ^{[1
]}

Koshlukov, Plamen ^{[2
]}

Krasilnikov, Alexei ^{[3
]}

da Silva, Elida Alves ^{[4
]}

机构：

[1] Univ Fed Campina Grande, UAME CCT, BR-58109970 Campina Grande, PB, Brazil

[2] Univ Estadual Campinas, IMECC, BR-13083970 Campinas, SP, Brazil

[3] Univ Brasilia, Dept Matemat, BR-70910900 Brasilia, DF, Brazil

[4] Univ Fed Goias, Dept Matemat, BR-75705220 Catalao, GO, Brazil

来源：

ISRAEL JOURNAL OF MATHEMATICS | 2010年 / 179卷 / 01期

基金：

巴西圣保罗研究基金会;

关键词：

IDENTITIES;

D O I：

10.1007/s11856-010-0074-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we describe the central polynomials for the infinite-dimensional unitary Grassmann algebra G over an infinite field F of characteristic not equal 2. We exhibit a set of polynomials that generates the vector space C( G) of the central polynomials of G as a T-space. Using a deep result of Shchigolev we prove that if char F = p > 2 then the T-space C( G) is not finitely generated. Moreover, over such a field F, C( G) is a limit T-space, that is, C( G) is not a finitely generated T-space but every larger T-space W not greater than or equal to C( G) is. We obtain similar results for the infinite-dimensional non-unitary Grassmann algebra H as well.

引用

页码：127 / 144

页数：18

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