矩阵中心化子中幂零元生成的代数

IF 0.7 4区数学 Q2 Mathematics

Electronic Journal of Linear Algebra Pub Date : 2021-12-23 DOI:10.13001/ela.2022.6503

Ralph John de la Cruz, Eloise Misa

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引用次数: 2

摘要

对于任意的平方矩阵$S$，用$C（S）$表示$S$的中心化子，用$C（S）_N$表示$C（S）$中所有幂零元素的集合。在本文中，我们使用Weyr正则形式来研究由$C（S）_N$生成的$C（S）$的子代数。我们确定了$S$上的条件，使得$C（S）_N$是$C（S）$的子代数。我们还确定了$S$上的条件，使得由$C（S）_N$生成的子代数是$C（S）$

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The algebra generated by nilpotent elements in a matrix centralizer

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 $C(S).$

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来源期刊

Electronic Journal of Linear Algebra 数学-数学

CiteScore

1.20

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal is essentially unlimited by size. Therefore, we have no restrictions on length of articles. Articles are submitted electronically. Refereeing of articles is conventional and of high standards. Posting of articles is immediate following acceptance, processing and final production approval.