Overgroups of subsystem subgroups in exceptional groups: 2A1-proof

P. Gvozdevsky
{"title":"Overgroups of subsystem subgroups in exceptional groups: 2A1-proof","authors":"P. Gvozdevsky","doi":"10.1090/spmj/1682","DOIUrl":null,"url":null,"abstract":"In the present paper we prove a weak form of sandwich classification for the overgroups of the subsystem subgroup $E(\\Delta,R)$ of the Chevalley group $G(\\Phi,R)$ where $\\Phi$ is a symply laced root sysetem and $\\Delta$ is its sufficiently large subsystem. Namely we show that for any such an overgroup $H$ there exists a unique net of ideals $\\sigma$ of the ring $R$ such that $E(\\Phi,\\Delta,R,\\sigma)\\le H\\le {\\mathop{\\mathrm{Stab}}\\nolimits}_{G(\\Phi,R)}(L(\\sigma))$ where $E(\\Phi,\\Delta,R,\\sigma)$ is an elementary subgroup associated with the net and $L(\\sigma)$ is a corresponding subalgebra of the Chevalley Lie algebra.","PeriodicalId":8427,"journal":{"name":"arXiv: Group Theory","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2019-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Group Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/spmj/1682","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2

Abstract

In the present paper we prove a weak form of sandwich classification for the overgroups of the subsystem subgroup $E(\Delta,R)$ of the Chevalley group $G(\Phi,R)$ where $\Phi$ is a symply laced root sysetem and $\Delta$ is its sufficiently large subsystem. Namely we show that for any such an overgroup $H$ there exists a unique net of ideals $\sigma$ of the ring $R$ such that $E(\Phi,\Delta,R,\sigma)\le H\le {\mathop{\mathrm{Stab}}\nolimits}_{G(\Phi,R)}(L(\sigma))$ where $E(\Phi,\Delta,R,\sigma)$ is an elementary subgroup associated with the net and $L(\sigma)$ is a corresponding subalgebra of the Chevalley Lie algebra.
例外群中子系统子群的过群:2a1证明
本文证明了Chevalley群$G(\Phi,R)$的子系统子群$E(\Delta,R)$的过群的一个弱形式的夹心分类,其中$\Phi$是一个单带根系统,$\Delta$是它的足够大子系统。也就是说,我们证明了对于任何这样的过群$H$,存在一个环$R$的唯一理想网$\sigma$,使得$E(\Phi,\Delta,R,\sigma)\le H\le {\mathop{\mathrm{Stab}}\nolimits}_{G(\Phi,R)}(L(\sigma))$,其中$E(\Phi,\Delta,R,\sigma)$是与网相关联的初等子群,$L(\sigma)$是Chevalley Lie代数的相应子代数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信