Codimension growth of central polynomials of Lie algebras

被引：0

作者：

Giambruno, Antonio ^{[1
]}

Zaicev, Mikhail ^{[2
]}

机构：

[1] Univ Palermo, Dipartimento Matemat & Informat, Via Archirafi 34, I-90123 Palermo, Italy

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

来源：

FORUM MATHEMATICUM | 2020年 / 32卷 / 01期

基金：

俄罗斯科学基金会;

关键词：

Central polynomial; polynomial identity; codimension; exponential growth; IDENTITIES;

D O I：

10.1515/forum-2019-0130

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let L be a finite-dimensional simple Lie algebra over an algebraically closed field of characteristic zero and let I be the T-ideal of polynomial identities of the adjoint representation of L. We prove that the number of multilinear central polynomials in n variables, linearly independent modulo I, grows exponentially like (dim L)(n).

引用

页码：201 / 206

页数：6

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