The images of Lie polynomials evaluated on matrices

被引：19

作者：

Kanel-Belov, Alexei ^{[1
]}

Malev, Sergey ^{[2
]}

Rowen, Louis ^{[1
]}

机构：

[1] Bar Ilan Univ, Dept Math, IL-52100 Ramat Gan, Israel

[2] Hebrew Univ Jerusalem, Einstein Inst Math, Jerusalem, Israel

来源：

COMMUNICATIONS IN ALGEBRA | 2017年 / 45卷 / 11期

基金：

以色列科学基金会;

关键词：

Lie polynomials; matrices; INVARIANT-THEORY; WORD MAPS;

D O I：

10.1080/00927872.2017.1282959

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Kaplansky asked about the possible images of a polynomial f in several noncommuting variables. In this paper, we consider the case of f a Lie polynomial. We describe all the possible images of f in M-2(K) and provide an example of f whose image is the set of non-nilpotent trace zero matrices, together with 0. We provide an arithmetic criterion for this case. We also show that the standard polynomial s(k) is not a Lie polynomial, for k>2.

引用

页码：4801 / 4808

页数：8

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