当前位置:
X-MOL 学术
›
J. Algebra Appl.
›
论文详情
Our official English website, www.x-mol.net, welcomes your
feedback! (Note: you will need to create a separate account there.)
The stabilizer of two-dimensional vector space of 27-dimensional module of type E6 over a field of characteristic two
Journal of Algebra and Its Applications ( IF 0.5 ) Pub Date : 2020-07-20 , DOI: 10.1142/s0219498821501516 Yousuf Alkhezi 1 , Mshhour Bani-Ata 1
Journal of Algebra and Its Applications ( IF 0.5 ) Pub Date : 2020-07-20 , DOI: 10.1142/s0219498821501516 Yousuf Alkhezi 1 , Mshhour Bani-Ata 1
Affiliation
The purpose of this paper is to use the notion of M -sets (cocliques) introduced by the second author in [S. Aldhafeeri and M. Bani-Ata, On the construction of Lie-algebras of type E 6 ( K ) for fields of characteristic two, Beitrag Zur Algebra und Geometry 58 (2017) 529–534.] and using Levi components and unipotent radical subgroups of E 6 ( K ) to give an elementary and self-contained construction of the stabilizer of two dimensional vector space of 27-dimensional module of type E 6 over a field of characteristic two. This stabilizer is in fact the maximal parabolic subgroup P 2 of E 6 or a Borel subgroup. This construction is elementary on the account that we use not more than little naive linear algebra notions. For more information one can see [M. E. Aschbacher, The 27-dimensional module for E 6 , 1, Invent. Math. 89 (1987) 159–195; M. E. Aschbacher, The 27-dimensional module for E 6 , II, J. London Math. Soc. 37 (1988) 275–293; M. Bani-Ata, On Lie algebras of type F 4 and D 4 over finite fields of characteristic two, Preprint; B. Cooperstein, Subgroups of the group E 6 ( q ) which are generated by root-subgroups, J. Algebra 46 (1977) 355–388.].
中文翻译:
E6型27维模的二维向量空间在特征二场上的稳定器
本文的目的是使用米 -sets (cocliques) 由第二作者在 [S. Aldhafeeri 和 M. Bani-Ata,关于类型李代数的构造乙 6 ( ķ ) 对于特征二的领域,Beitrag Zur 代数和几何 58 (2017) 529–534.] 并使用 Levi 组件和单能自由基子群乙 6 ( ķ ) 给出类型为 27 维模的二维向量空间稳定器的基本且自包含的构造乙 6 在特征二的领域。这个稳定器实际上是最大抛物线子群磷 2 的乙 6 或 Borel 子群。这种构造是基本的,因为我们使用的只是很少的朴素线性代数概念。有关更多信息,请参阅 [ME Aschbacher, The 27-dimensional module for乙 6 , 1,发明。数学。 89 (1987) 159–195;ME Aschbacher,27 维模块乙 6 , 二,J.伦敦数学。社会党。 37 (1988) 275–293;M. Bani-Ata,关于类型的李代数F 4 和D 4 在特征二的有限域上,预印本;B. Cooperstein,小组的子组乙 6 ( q ) 由根子组生成,J.代数 46 (1977) 355–388.]。
更新日期:2020-07-20
中文翻译:
E6型27维模的二维向量空间在特征二场上的稳定器
本文的目的是使用