Complexity for modules over finite Chevalley groups and classical Lie algebras

1999 ◽  
Vol 138 (1) ◽  
pp. 85-101 ◽  
Author(s):  
Zongzhu Lin ◽  
Daniel K. Nakano
Keyword(s):  
Lie Algebras ◽  
Chevalley Groups

scholarly journals Support varieties for modules over Chevalley groups and classical Lie algebras

2007 ◽  
Vol 360 (04) ◽  
pp. 1879-1907
Author(s):  
Jon F. Carlson ◽  
Zongzhu Lin ◽  
Daniel K. Nakano
Keyword(s):  
Lie Algebras ◽  
Chevalley Groups ◽  
Support Varieties

On root-involutions and root-subgroups of E6(K) for fields K of characteristic two

2019 ◽  
Vol 18 (01) ◽  
pp. 1950017 ◽  
Author(s):  
S. Aldhafeeri ◽  
M. Bani-Ata
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Linear Algebra ◽  
Chevalley Group ◽  
Chevalley Groups ◽  
Type Formula ◽  
Characteristic Two

The purpose of this paper is to investigate the root-involutions and root-subgroups of the Chevalley group [Formula: see text] for fields [Formula: see text] of characteristic two. The approach we follow is elementary and self-contained depends on the notion of [Formula: see text]-sets which we have introduced in [Aldhafeeri and M. Bani-Ata, On the construction of Lie-algebras of type [Formula: see text] for fields of characteristic two, Beit. Algebra Geom. 58 (2017) 529–534]. The approach is elementary on the account that it consists of little more than naive linear algebra. It is remarkable to mention that Chevalley groups over fields of characteristic two have not much been researched. This work may contribute in this regard. This paper is divided into three main sections: the first section is a combinatorial section, the second section is on relations among [Formula: see text]-sets, the last one is on Lie algebra.

scholarly journals A family of simple groups associated with the Satake diagrams

1986 ◽  
Vol 41 (1) ◽  
pp. 13-43 ◽  
Author(s):  
Cheng Chonhu
Keyword(s):  
Lie Algebras ◽  
Number Field ◽  
Complex Number ◽  
Algebraic Groups ◽  
Simple Groups ◽  
Orthogonal Groups ◽  
Bruhat Decomposition ◽  
Chevalley Groups ◽  
Complex Number Field ◽  
Real Number Field

AbstractUsing the theory of the Satake diagrams associated with the non-compact simple Lie algebras over the real number field R, we shall construct a family of simple groups over a field K which are called the simple groups associated with the Satake diagrams. The list of these simple groups includes all Chevalley groups and twisted groups, and all simple algebraic groups of adjoint type defined over R if K is the complex number field C (except two types given by Table II′). Furthermore, the simple groups associated with the Satake diagrams of type AIII, BI, DI are identified with the simple groups obtained from the unitary or orthogonal groups of non-zero indices. The quasi-Bruhat decomposition of the “non-split” simple groups associated with the Satake diagrams which are not Chevalley groups or twisted groups will be given in this paper.

scholarly journals The Highest Dimension of Commutative Subalgebras in Chevalley Algebras

2019 ◽  
pp. 351-354
Author(s):  
Galina S. Suleimanova
Keyword(s):  
Root System ◽  
Lie Groups ◽  
Lie Algebras ◽  
Arbitrary Field ◽  
Chevalley Groups ◽  
Simple Lie Groups ◽  
Abelian Subgroups ◽  
Commutative Subalgebras

Let L (K) denotes a Chevalley algebra with the root system over a field K. In 1945 A. I. Mal’cev investigated the problem of describing abelian subgroups of highest dimension in complex simple Lie groups. He solved this problem by transition to complex Lie algebras and by reduction to the problem of describing commutative subalgebras of highest dimension in the niltriangular subalgebra. Later these methods were modified and applied for the problem of describing large abelian subgroups in finite Chevalley groups. The main result of this article allows to calculate the highest dimension of commutative subalgebras in a Chevalley algebra L (K) over an arbitrary field

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