A geometry of the generalized quadrangle (Ω, L) of type O6- (2) and Lie algebras of type E6 with characteristic two

被引：4

作者：

Alkhezi, Yousuf ^{[1
]}

Ata, Mashhour Bani ^{[1
]}

机构：

[1] Coll Basic Educ Publ Author Appl Educ & Training, Dept Math, Kuwait, Kuwait

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2020年 / 19卷 / 01期

关键词：

Lie groups; Lie algebras; generalized quadrangles; Chevalley groups; 27-DIMENSIONAL MODULE;

D O I：

10.1142/S0219498820500164

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this paper is to study certain geometric properties of generalized quadrangle (Omega, L) of type O-6(-) (2). We define certain root elements which generate a Lie algebra of type E-6(K) for fields K of characteristic two. The construction will be mainly based on the geometric properties of the generalized quadrangle (Omega, L). In fact, we will explicity construct a Chevalley base of this Lie algebra.

引用

页数：13

共 15 条

[1] On Lie algebras of type F4 and Chevalley groups F4(K), E6(K), and 2E6(K) for fields K of characteristic two
Al-dhafeeri, Shuaa
Ata, Mashhour Bani
COMMUNICATIONS IN ALGEBRA, 2019, 47 (02) : 516 - 522
[2] GEOMETRY OF ROOT ELEMENTS IN GROUPS OF TYPE E6
Pevzner, I. M.
ST PETERSBURG MATHEMATICAL JOURNAL, 2012, 23 (03) : 603 - 635
[3] NORMALIZER OF THE CHEVALLEY GROUP OF TYPE E6
Vavilov, N. A.
Luzgarev, A. Yu.
ST PETERSBURG MATHEMATICAL JOURNAL, 2008, 19 (05) : 699 - 718
[4] The stabilizer of two-dimensional vector space of 27-dimensional module of type E6 over a field of characteristic two
Alkhezi, Yousuf
Bani-Ata, Mshhour
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2021, 20 (08)
[5] Quadratic Forms on the 27-Dimensional Modules for E6 in Characteristic Two
Bani-Ata, Mashhour
JOURNAL OF LIE THEORY, 2022, 32 (01) : 75 - 86
[6] On the computation of the nilpotent pieces in bad characteristic for algebraic groups of type G2, F4, and E6
Voggesberger, Laura
JOURNAL OF ALGEBRA, 2023, 617 : 48 - 78
[7] Root elements and root subgroups in E6(K) for fields K of characteristic two
Alhuraiji, Abdulkareem
Bani-Ata, Mashhour Al -Ali
INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE, 2024, 19 (01) : 219 - 227
[8] WIDTH OF GROUPS OF TYPE E6 WITH RESPECT TO ROOT ELEMENTS. I
Pevzner, I. M.
ST PETERSBURG MATHEMATICAL JOURNAL, 2012, 23 (05) : 891 - 919
[9] On pairs of root groups and reflections associated to the Chevalley group E6(K), in characteristic two
Kasasbeh, Khaled Ali Ahmad
Bani-Ata, Mashhour Al-Ali
COMMUNICATIONS IN ALGEBRA, 2025, 53 (04) : 1612 - 1619
[10] On construction of maximal parabolic centralizers of root elements and the Weyl group of type F4 in E6(K) for fields K of characteristic 2
Alhuraiji, Abdulkareem
Bani-Ata, Mashhour Al-Ali
KUWAIT JOURNAL OF SCIENCE, 2023, 50 (04) : 439 - 442

← 1 2 →