幂零轨道代表的稳定器组成群的计算

IF 0.6 4区数学 Q4 COMPUTER SCIENCE, THEORY & METHODS Journal of Symbolic Computation Pub Date : 2024-11-26 DOI:10.1016/j.jsc.2024.102404

Emanuele Di Bella, Willem A. de Graaf

{"title":"幂零轨道代表的稳定器组成群的计算","authors":"Emanuele Di Bella, Willem A. de Graaf","doi":"10.1016/j.jsc.2024.102404","DOIUrl":null,"url":null,"abstract":"<div><div>We describe computational methods for computing the component group of the stabilizer of a nilpotent element in a complex simple Lie algebra. Our algorithms have been implemented in the language of the computer algebra system <span>GAP</span>4. Occasionally we need Gröbner basis computations; for these we use the systems <span>Magma</span> and <span>Singular</span>. The resulting component groups have been made available in the <span>GAP</span>4 package <span>SLA</span>.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"129 ","pages":"Article 102404"},"PeriodicalIF":0.6000,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Computing component groups of stabilizers of nilpotent orbit representatives\",\"authors\":\"Emanuele Di Bella, Willem A. de Graaf\",\"doi\":\"10.1016/j.jsc.2024.102404\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We describe computational methods for computing the component group of the stabilizer of a nilpotent element in a complex simple Lie algebra. Our algorithms have been implemented in the language of the computer algebra system <span>GAP</span>4. Occasionally we need Gröbner basis computations; for these we use the systems <span>Magma</span> and <span>Singular</span>. The resulting component groups have been made available in the <span>GAP</span>4 package <span>SLA</span>.</div></div>\",\"PeriodicalId\":50031,\"journal\":{\"name\":\"Journal of Symbolic Computation\",\"volume\":\"129 \",\"pages\":\"Article 102404\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-11-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Symbolic Computation\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0747717124001081\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Symbolic Computation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0747717124001081","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}

引用次数: 0

摘要

描述了复单李代数中幂零元稳定器的组成群的计算方法。我们的算法已在计算机代数系统GAP4语言中实现。偶尔我们需要Gröbner基计算；对于这些，我们使用Magma和Singular系统。生成的组件组已在GAP4包SLA中提供。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Computing component groups of stabilizers of nilpotent orbit representatives

We describe computational methods for computing the component group of the stabilizer of a nilpotent element in a complex simple Lie algebra. Our algorithms have been implemented in the language of the computer algebra system GAP4. Occasionally we need Gröbner basis computations; for these we use the systems Magma and Singular. The resulting component groups have been made available in the GAP4 package SLA.

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

来源期刊

Journal of Symbolic Computation 工程技术-计算机：理论方法

CiteScore

2.10

自引率

14.30%

发文量

审稿时长

142 days

期刊介绍： An international journal, the Journal of Symbolic Computation, founded by Bruno Buchberger in 1985, is directed to mathematicians and computer scientists who have a particular interest in symbolic computation. The journal provides a forum for research in the algorithmic treatment of all types of symbolic objects: objects in formal languages (terms, formulas, programs); algebraic objects (elements in basic number domains, polynomials, residue classes, etc.); and geometrical objects. It is the explicit goal of the journal to promote the integration of symbolic computation by establishing one common avenue of communication for researchers working in the different subareas. It is also important that the algorithmic achievements of these areas should be made available to the human problem-solver in integrated software systems for symbolic computation. To help this integration, the journal publishes invited tutorial surveys as well as Applications Letters and System Descriptions.

期刊最新文献

Computing component groups of stabilizers of nilpotent orbit representatives Editorial Board Computing the homology of universal covers via effective homology and discrete vector fields Local dual spaces and primary decomposition On the existence and convergence of formal power series solutions of nonlinear Mahler equations