矩阵中心化子中幂零元生成的代数

Pub Date : 2021-12-23 DOI:10.13001/ela.2022.6503

Ralph John de la Cruz, Eloise Misa

{"title":"矩阵中心化子中幂零元生成的代数","authors":"Ralph John de la Cruz, Eloise Misa","doi":"10.13001/ela.2022.6503","DOIUrl":null,"url":null,"abstract":"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 $C(S).$","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"The algebra generated by nilpotent elements in a matrix centralizer\",\"authors\":\"Ralph John de la Cruz, Eloise Misa\",\"doi\":\"10.13001/ela.2022.6503\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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 $C(S).$\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2021-12-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.13001/ela.2022.6503\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.13001/ela.2022.6503","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

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$C（S）$

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

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 $C(S).$

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助