scholarly journals Classification of simple Lie algebras on a lattice

2012 ◽  
Vol 106 (3) ◽  
pp. 508-564 ◽  
Author(s):  
Kenji Iohara ◽  
Olivier Mathieu
Keyword(s):  
Lie Algebras ◽  
Simple Lie Algebras

scholarly journals Classification of the restricted simple Lie algebras

1988 ◽  
Vol 114 (1) ◽  
pp. 115-259 ◽  
Author(s):  
Richard E Block ◽  
Robert Lee Wilson
Keyword(s):  
Lie Algebras ◽  
Simple Lie Algebras

On constructions of Lie (super) algebras and (𝜀,δ)-Freudenthal–Kantor triple systems defined by bilinear forms

2019 ◽  
Vol 19 (11) ◽  
pp. 2050223
Author(s):  
Noriaki Kamiya ◽  
Daniel Mondoc
Keyword(s):  
Lie Algebras ◽  
Complex Structure ◽  
Bilinear Forms ◽  
Simple Lie Algebras ◽  
Triple Systems ◽  
Dynkin Diagrams

In this work, we discuss a classification of [Formula: see text]-Freudenthal–Kantor triple systems defined by bilinear forms and give all examples of such triple systems. From these results, we may see a construction of some simple Lie algebras or superalgebras associated with their Freudenthal–Kantor triple systems. We also show that we can associate a complex structure into these ([Formula: see text]-Freudenthal–Kantor triple systems. Further, we introduce the concept of Dynkin diagrams associated to such [Formula: see text]-Freudenthal–Kantor triple systems and the corresponding Lie (super) algebra construction.

Classification of forms of restricted simple lie algebras of cartan type

1991 ◽  
Vol 19 (6) ◽  
pp. 1603-1628 ◽  
Author(s):  
Shirlei Serconek ◽  
Robert Lee Wilson
Keyword(s):  
Lie Algebras ◽  
Simple Lie Algebras ◽  
Cartan Type
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