Simple Classical Lie Algebras in Characteristic 2 and Their Gradations, II

2014 ◽  
Vol 21 (02) ◽  
pp. 207-214
Author(s):  
Alexandre N. Grishkov ◽  
Marinês Guerreiro
Keyword(s):  
Lie Algebras ◽  
Finite Dimension ◽  
Type B ◽  
Simple Lie Algebras ◽  
Characteristic 2

This paper is a continuation of [2]. We prove Conjecture 5.1 of [2] which gives a characterization of simple Lie algebras of finite dimension of type B2ℓ, C2ℓ, D2ℓ+1, E7 and E8 in terms of some gradations of these algebras over a field of characteristic 2.

scholarly journals CODES, S-STRUCTURES, AND EXCEPTIONAL LIE ALGEBRAS

2019 ◽  
Vol 62 (S1) ◽  
pp. S14-S27 ◽  
Author(s):  
ISABEL CUNHA ◽  
ALBERTO ELDUQUE
Keyword(s):  
Lie Algebras ◽  
Simple Lie Algebras ◽  
Nonassociative Algebras ◽  
Exceptional Lie Algebras

AbstractThe exceptional simple Lie algebras of types E7 and E8 are endowed with optimal $\mathsf{SL}_2^n$ -structures, and are thus described in terms of the corresponding coordinate algebras. These are nonassociative algebras which much resemble the so-called code algebras.

Models of isotropic simple lie algebras

1979 ◽  
Vol 7 (17) ◽  
pp. 1835-1875 ◽  
Author(s):  
B.N. Allison
Keyword(s):  
Lie Algebras ◽  
Simple Lie Algebras
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