Generators of simple graded Lie algebras of finite growth

2017 ◽  
Vol 148 (2) ◽  
pp. 315-324
Author(s):  
Liming Tang ◽  
Wende Liu
Keyword(s):  
Lie Algebras ◽  
Graded Lie Algebras ◽  
Finite Growth

Hom-structures on simple graded Lie algebras of finite growth

2016 ◽  
Vol 16 (08) ◽  
pp. 1750154 ◽  
Author(s):  
Wenjuan Xie ◽  
Wende Liu
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Jordan Algebra ◽  
Jacobi Identity ◽  
Direct Consequence ◽  
Classification Theorem ◽  
Algebra Homomorphism ◽  
Graded Lie Algebras ◽  
Linear Map ◽  
Finite Growth

A Hom-structure on a Lie algebra [Formula: see text] is a linear map [Formula: see text] satisfying the Hom–Jacobi identity: [Formula: see text] for all [Formula: see text]. A Hom-structure is referred to as multiplicative if it is also a Lie algebra homomorphism. In this paper, using a classification theorem due to Mathieu, we determine explicitly all the Hom-structures on the simple graded Lie algebras of finite growth. As a direct consequence, all the Hom-structures on any simple graded Lie algebras of finite growth constitute a Jordan algebra in the usual way.

Cohomology of certain $ \mathbb N$-graded Lie algebras

2004 ◽  
Vol 59 (6) ◽  
pp. 1210-1211
Author(s):  
D V Millionshchikov ◽  
A Fialowski
Keyword(s):  
Lie Algebras ◽  
Graded Lie Algebras

scholarly journals Graded Lie Algebras of Maximal Class

1997 ◽  
Vol 349 (10) ◽  
pp. 4021-4051 ◽  
Author(s):  
A. Caranti ◽  
S. Mattarei ◽  
M. F. Newman
Keyword(s):  
Lie Algebras ◽  
Maximal Class ◽  
Graded Lie Algebras
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