THE ALGEBRA GENERATED BY NILPOTENT ELEMENTS IN A MATRIX CENTRALIZER

被引：0

作者：

de la Cruz, Ralph John ^{[1
]}

Misa, Eloise ^{[1
]}

机构：

[1] Univ Philippines, Inst Math, Quezon City, Philippines

来源：

ELECTRONIC JOURNAL OF LINEAR ALGEBRA | 2022年 / 38卷

关键词：

Nilpotent; Weyr form; Centralizer; Matrix decompositions; PRODUCTS; SUMS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For an arbitrary square matrix S, denote by C(S) the centralizer of S, and by C(S)(N) the set of all nilpotent elements in C(S). In this paper, we use the Weyr canonical form to study the subalgebra of C(S) generated by C(S)(N). We determine conditions on S such that C(S)(N) is a subalgebra of C(S). We also determine conditions on S such that the subalgebra generated by C(S)(N) is C(S).

引用

页码：1 / 8

页数：8

共 50 条

[1] THE ALGEBRA GENERATED BY SIMPLE ELEMENTS OF A MATRIX CENTRALIZER
de la Cruz, Ralph John
[J]. OPERATORS AND MATRICES, 2021, 15 (02): : 677 - 684
[2] The index of a Lie algebra, the centralizer of a nilpotent element, and the normalizer of the centralizer
Panyushev, DI
[J]. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2003, 134 : 41 - 59
[3] On the centralizer of the sum of commuting nilpotent elements
McNinch, G
[J]. JOURNAL OF PURE AND APPLIED ALGEBRA, 2006, 206 (1-2) : 123 - 140
[4] The Cartan matrix of a centralizer algebra
UMESH V DUBEY
AMRITANSHU PRASAD
POOJA SINGLA
[J]. Proceedings - Mathematical Sciences, 2012, 122 : 67 - 73
[5] The Cartan matrix of a centralizer algebra
Dubey, Umesh V.
Prasad, Amritanshu
Singla, Pooja
[J]. PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2012, 122 (01): : 67 - 73
[6] ON THE MAXIMAL NILPOTENT ORBIT THAT INTERSECTS THE CENTRALIZER OF A MATRIX
ROBERTA BASILI
[J]. Transformation Groups, 2022, 27 : 1 - 30
[7] ON THE MAXIMAL NILPOTENT ORBIT THAT INTERSECTS THE CENTRALIZER OF A MATRIX
Basili, Roberta
[J]. TRANSFORMATION GROUPS, 2022, 27 (01) : 1 - 30
[8] WEYL ALGEBRA - SEMISIMPLE AND NILPOTENT ELEMENTS
JOSEPH, A
[J]. AMERICAN JOURNAL OF MATHEMATICS, 1975, 97 (03) : 597 - 615
[9] NILPOTENT ELEMENTS OF A FREE JORDAN ALGEBRA
MEDVEDEV, YA
[J]. SIBERIAN MATHEMATICAL JOURNAL, 1985, 26 (02) : 271 - 277
[10] The centralizer of a nilpotent section
Mcninch, George J.
[J]. NAGOYA MATHEMATICAL JOURNAL, 2008, 190 : 129 - 181

← 1 2 3 4 5 →