Overgroups of subsystem subgroups in exceptional groups: nonideal levels

Author:

Gvozdevsky P.

Abstract

In the present paper, a description of overgroups for the subsystem subgroups E ( Δ , R ) E(\Delta ,R) of the Chevalley groups G ( Φ , R ) G(\Phi ,R) over the ring R R , where Φ \Phi is a simply laced root system and Δ \Delta is its sufficiently large subsystem, is almost entirely finished. Namely, objects called levels are defined and it is shown that for any such overgroup H H there exists a unique level σ \sigma with E ( σ ) H Stab G ( Φ , R ) ( L max ( σ ) ) E(\sigma )\le H\le \operatorname {Stab}_{G(\Phi ,R)}(L_{\max }(\sigma )) , where E ( σ ) E(\sigma ) is an elementary subgroup associated with the level σ \sigma and L max ( σ ) L_{\max }(\sigma ) is the corresponding subalgebra of the Chevalley algebra. Unlike the previous papers, here levels can be more complicated than nets of ideals.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Algebra and Number Theory,Analysis

Reference27 articles.

1. Arrangement of subgroups in the general linear group over a commutative ring;Borevich, Z. I.;Trudy Mat. Inst. Steklov.,1984

2. Actualit\'{e}s Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1337;Bourbaki, N.,1968

3. Subgroups of split orthogonal groups over a ring;Vavilov, N. A.;Sibirsk. Mat. Zh.,1988

4. Subgroups of splittable classical groups;Vavilov, N. A.;Trudy Mat. Inst. Steklov.,1990

5. On overgroups of 𝐸𝑝(2𝑙,𝑅);Vavilov, N. A.;Algebra i Analiz,2003

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Overgroups of subsystem subgroups in exceptional groups: nonideal levels;St. Petersburg Mathematical Journal;2022-10-31

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3