IMAGES OF MULTILINEAR POLYNOMIALS OF DEGREE UP TO FOUR ON UPPER TRIANGULAR MATRICES

被引：16

作者：

Fagundes, Pedro S. ^{[1
]}

de Mello, Thiago C. ^{[1
]}

机构：

[1] Univ Fed Sao Paulo, Inst Ciencia & Tecnol, Sao Paulo, Brazil

来源：

OPERATORS AND MATRICES | 2019年 / 13卷 / 01期

基金：

巴西圣保罗研究基金会;

关键词：

Images of polynomials; upper triangular matrices; Lvov-Kaplansky conjecture;

D O I：

10.7153/oam-2019-13-18

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We describe the images of multilinear polynomials of degree up to four on the upper triangular matrix algebra.

引用

页码：283 / 292

页数：10

共 10 条

[1]

Albert Abraham Adrian, 1957, Mich. Math. J., V4, P1, DOI DOI 10.1307/MMJ/1028990168

[2] ELEMENTS OF REDUCED TRACE 0 [J].

Amitsur, S. A. ;

Rowen, Louis H. .

ISRAEL JOURNAL OF MATHEMATICS, 1994, 87 (1-3) :161-179

[3] On multilinear polynomials in four variables evaluated on matrices [J].

Buzinski, David ;

Winstanley, Robin .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2013, 439 (09) :2712-2719

[4]

FALK G., 1952, MATH ANN, V124, P182

[5]

Filippov V.T., 2006, DNIESTER NOTEBOOK UN, V246, P461

[6] A BASIS FOR FREE LIE RINGS AND HIGHER COMMUTATORS IN FREE GROUPS [J].

HALL, M .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1950, 1 (05) :575-581

[7] 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

[8] Polynomials of small degree evaluated on matrices [J].

Mesyan, Zachary .

LINEAR & MULTILINEAR ALGEBRA, 2013, 61 (11) :1487-1495

[9]

Shoda K., 1937, Jpn. J. Math., V13, P361

[10] On the image of a noncommutative polynomial [J].

Spenko, Spela .

JOURNAL OF ALGEBRA, 2013, 377 :298-311

← 1 →