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).
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页码：201 / 206
页数：6
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