Power-central polynomials on matrices

被引：17

作者：

Kanel-Belov, Alexey ^{[1
]}

Malev, Sergey ^{[1
,2
]}

Rowen, Louis ^{[1
]}

机构：

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

[2] Univ Edinburgh, Edinburgh, Midlothian, Scotland

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2016年 / 220卷 / 06期

基金：

以色列科学基金会;

关键词：

D O I：

10.1016/j.jpaa.2015.11.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Any multilinear non-central polynomial p (in several noncommuting variables) takes on values of degree n in the matrix algebra M-n(F) over an infinite field F. The polynomial p is called v-central for M-n(F) if p(v) takes on only scalar values, with v minimal such. Multilinear v-central polynomials do not exist for any v, with n > 3, answering a question of Drensky and Spenko. Saltman proved a result implying that a non-central polynomial p cannot be v-central for M-n(F), for n odd, unless v is a product of distinct odd primes and n = mv with m prime to v; we extend this by showing for n even, that v cannot be divisible by 4. (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：2164 / 2176

页数：13