The image of polynomials on 2 x 2 upper triangular matrix algebras

被引：9

作者：

Wang, Yu ^{[1
]}

Zhou, Jia ^{[1
]}

Luo, Yingyu ^{[1
]}

机构：

[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2021年 / 610卷

关键词：

Lvov-Kaplansky Conjecture; Polynomial; Upper triangular matrix algebra;

D O I：

10.1016/j.laa.2020.10.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The goal of the paper is to give a complete description of the image of polynomials with zero constant term on 2 x 2 upper triangular matrix algebras over an algebraically closed field. (C) 2020 Elsevier Inc. All rights reserved.

引用

页码：560 / 570

页数：11

共 14 条

[1] On the images of Lie polynomials evaluated on Lie algebras [J].

Anzis, Benjamin E. ;

Emrich, Zachary M. ;

Valiveti, Kaavya G. .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2015, 469 :51-75

[2]

Drensky V., 1996, FREE ALGEBRAS PI ALG, P1

[3] IMAGES OF MULTILINEAR POLYNOMIALS OF DEGREE UP TO FOUR ON UPPER TRIANGULAR MATRICES [J].

Fagundes, Pedro S. ;

de Mello, Thiago C. .

OPERATORS AND MATRICES, 2019, 13 (01) :283-292

[4] The images of multilinear polynomials on strictly upper triangular matrices [J].

Fagundes, Pedro S. .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2019, 563 :287-301

[5] The images of Lie polynomials evaluated on matrices [J].

Kanel-Belov, Alexei ;

Malev, Sergey ;

Rowen, Louis .

COMMUNICATIONS IN ALGEBRA, 2017, 45 (11) :4801-4808

[6] Power-central polynomials on matrices [J].

Kanel-Belov, Alexey ;

Malev, Sergey ;

Rowen, Louis .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2016, 220 (06) :2164-2176

[7] THE IMAGES OF MULTILINEAR POLYNOMIALS EVALUATED ON 3 x 3 MATRICES [J].

Kanel-Belov, Alexey ;

Malev, Sergey ;

Rowen, Louis .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 144 (01) :7-19

[8] THE IMAGES OF NON-COMMUTATIVE POLYNOMIALS EVALUATED ON 2 x 2 MATRICES [J].

Kanel-Belov, Alexey ;

Malev, Sergey ;

Rowen, Louis .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2012, 140 (02) :465-478

[9] On the images of Jordan polynomials evaluated over symmetric matrices [J].

Ma, Alexander ;

Oliva, Jamie .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2016, 492 :13-25

[10] The images of non-commutative polynomials evaluated on 2 x 2 matrices over an arbitrary field [J].

Malev, Sergey .

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2014, 13 (06)

← 1 2 →