扩展仿射李代数的字符：一种组合方法

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Algebraic Combinatorics Pub Date : 2024-05-06 DOI:10.1007/s10801-024-01325-y

Saeid Azam

{"title":"扩展仿射李代数的字符：一种组合方法","authors":"Saeid Azam","doi":"10.1007/s10801-024-01325-y","DOIUrl":null,"url":null,"abstract":"<p>The behavior of objects associated with general extended affine Lie algebras is typically distinct from their counterparts in affine Lie algebras. Our research focuses on studying characters and Cartan automorphisms, which appear in the study of Chevalley involutions and Chevalley bases for extended affine Lie algebras. We show that for almost all extended affine Lie algebras, any finite-order Cartan automorphism is diagonal, and its corresponding combinatorial map is a character.</p>","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Characters for extended affine Lie algebras: a combinatorial approach\",\"authors\":\"Saeid Azam\",\"doi\":\"10.1007/s10801-024-01325-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The behavior of objects associated with general extended affine Lie algebras is typically distinct from their counterparts in affine Lie algebras. Our research focuses on studying characters and Cartan automorphisms, which appear in the study of Chevalley involutions and Chevalley bases for extended affine Lie algebras. We show that for almost all extended affine Lie algebras, any finite-order Cartan automorphism is diagonal, and its corresponding combinatorial map is a character.</p>\",\"PeriodicalId\":14926,\"journal\":{\"name\":\"Journal of Algebraic Combinatorics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-05-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebraic Combinatorics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10801-024-01325-y\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebraic Combinatorics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10801-024-01325-y","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

与一般扩展仿射李代数相关的对象的行为通常不同于它们在仿射李代数中的对应物。我们的研究重点是研究扩展仿射李代数的切瓦利渐开线和切瓦利基中出现的character 和 Cartan 自动态。我们证明，对于几乎所有的扩展仿射李代数，任何有限阶 Cartan 自变量都是对角的，其相应的组合映射是一个字符。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Characters for extended affine Lie algebras: a combinatorial approach

The behavior of objects associated with general extended affine Lie algebras is typically distinct from their counterparts in affine Lie algebras. Our research focuses on studying characters and Cartan automorphisms, which appear in the study of Chevalley involutions and Chevalley bases for extended affine Lie algebras. We show that for almost all extended affine Lie algebras, any finite-order Cartan automorphism is diagonal, and its corresponding combinatorial map is a character.

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 Algebraic Combinatorics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Algebraic Combinatorics provides a single forum for papers on algebraic combinatorics which, at present, are distributed throughout a number of journals. Within the last decade or so, algebraic combinatorics has evolved into a mature, established and identifiable area of mathematics. Research contributions in the field are increasingly seen to have substantial links with other areas of mathematics. The journal publishes papers in which combinatorics and algebra interact in a significant and interesting fashion. This interaction might occur through the study of combinatorial structures using algebraic methods, or the application of combinatorial methods to algebraic problems.