Biderivations and strong commutativity-preserving maps on parabolic subalgebras of simple Lie algebras

2020 ◽  
pp. 1-13
Author(s):  
Zhengxin Chen ◽  
Yalong Yu
Keyword(s):  
Lie Algebras ◽  
Simple Lie Algebras ◽  
Parabolic Subalgebras ◽  
Strong Commutativity Preserving ◽  
Strong Commutativity

Strong commutativity preserving maps of strictly triangular matrix Lie algebras

2019 ◽  
Vol 18 (07) ◽  
pp. 1950134
Author(s):  
Zhengxin Chen ◽  
Hongjin Liu
Keyword(s):  
Linear Function ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Triangular Matrix ◽  
Linear Map ◽  
Strong Commutativity Preserving ◽  
Strong Commutativity

Let [Formula: see text] be the Lie algebra consisting of all strictly upper triangular [Formula: see text] matrices over a field [Formula: see text]. An invertible linear map [Formula: see text] on [Formula: see text] is called to be strong commutativity preserving (simply denoted by SCP) if [Formula: see text] for any [Formula: see text]. We show that for [Formula: see text], an invertible linear map [Formula: see text] preserves strong commutativity if and only if there exist [Formula: see text] and a linear function [Formula: see text] with [Formula: see text] such that [Formula: see text], where [Formula: see text] is an inner SCP, [Formula: see text] are extremal SCPs, [Formula: see text] is a central SCP.

Biderivations of the Parabolic Subalgebras of Simple Lie Algebras

2011 ◽  
Vol 39 (11) ◽  
pp. 4097-4104 ◽  
Author(s):  
Dengyin Wang ◽  
Xiaoxiang Yu ◽  
Zhengxin Chen
Keyword(s):  
Lie Algebras ◽  
Simple Lie Algebras ◽  
Parabolic Subalgebras

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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