Lie Groups and Symmetric Spaces, the Classification of Real Semi-Simple Lie Algebras and Symmetric Spaces

2017 ◽  
pp. 131-152
Keyword(s):  
Lie Groups ◽  
Lie Algebras ◽  
Symmetric Spaces ◽  
Simple Lie Algebras

scholarly journals Classification of Symmetry Lie Algebras of the Canonical Geodesic Equations of Five-Dimensional Solvable Lie Algebras

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1354 ◽  
Author(s):  
Hassan Almusawa ◽  
Ryad Ghanam ◽  
Gerard Thompson
Keyword(s):  
Lie Groups ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Vector Fields ◽  
Solvable Lie Groups ◽  
Related System ◽  
Geodesic Equations ◽  
Solvable Lie Algebras ◽  
Symmetry Algebras

In this investigation, we present symmetry algebras of the canonical geodesic equations of the indecomposable solvable Lie groups of dimension five, confined to algebras A 5 , 7 a b c to A 18 a . For each algebra, the related system of geodesics is provided. Moreover, a basis for the associated Lie algebra of the symmetry vector fields, as well as the corresponding nonzero brackets, are constructed and categorized.

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

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
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