THE IMAGES OF MULTILINEAR POLYNOMIALS EVALUATED ON 3 x 3 MATRICES

被引：28

作者：

Kanel-Belov, Alexey ^{[1
]}

Malev, Sergey ^{[1
]}

Rowen, Louis ^{[1
]}

机构：

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

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2016年 / 144卷 / 01期

基金：

以色列科学基金会;

关键词：

Noncommutative polynomial; image; multilinear; matrices; WORD MAPS;

D O I：

10.1090/proc/12478

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let p be a multilinear polynomial in several noncommuting variables, with coefficients in an algebraically closed field K of arbitrary characteristic. In this paper we classify the possible images of p evaluated on 3 x 3 matrices. The image is one of the following: {0}, the set of scalar matrices, a (Zariski-) dense subset of sl(3)(K), the matrices of trace 0, a dense subset of M-3(K), the set of 3-scalar matrices (i.e., matrices having eigenvalues (beta, beta epsilon, beta epsilon(2)) where epsilon is a cube root of 1), or the set of scalars plus 3-scalar matrices.

引用

页码：7 / 19

页数：13

共 18 条

[1]

Albert A.A., 1957, Mich. Math. J., V4, P1

[2] Word equations in simple groups and polynomial equations in simple algebras [J].