Non-Alternating Hamiltonian Lie Algebras of Characteristic Two in Three Variables

2021 ◽  
Vol 42 (12) ◽  
pp. 2841-2853
Author(s):  
A. V. Kondrateva
Keyword(s):  
Lie Algebras ◽  
Characteristic Two

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

2019 ◽  
Vol 19 (01) ◽  
pp. 2050016
Author(s):  
Yousuf Alkhezi ◽  
Mashhour Bani Ata
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Generalized Quadrangle ◽  
Geometric Properties ◽  
Type Formula ◽  
Characteristic Two

The purpose of this paper is to study certain geometric properties of generalized quadrangle [Formula: see text] of type [Formula: see text]. We define certain root elements which generate a Lie algebra of type [Formula: see text] for fields [Formula: see text] of characteristic two. The construction will be mainly based on the geometric properties of the generalized quadrangle [Formula: see text]. In fact, we will explicity construct a Chevalley base of this Lie algebra.

Binary Lie algebras of characteristic two

1969 ◽  
Vol 8 (5) ◽  
pp. 287-297 ◽  
Author(s):  
A. T. Gainov
Keyword(s):  
Lie Algebras ◽  
Characteristic Two

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.

Simple 14-Dimensional Lie Algebras in Characteristic Two

2019 ◽  
Vol 240 (4) ◽  
pp. 474-480 ◽  
Author(s):  
M. I. Kuznetsov ◽  
A. V. Kondrateva ◽  
N. G. Chebochko
Keyword(s):  
Lie Algebras ◽  
Characteristic Two
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