| gptkbp:instanceOf | gptkb:mathematical_concept 
 | 
                        
                            
                                | gptkbp:ariseIn | gptkb:octonion_algebra gptkb:string_theory
 theory of Lie groups
 grand unified theories
 theory of Lie algebras
 Lie algebra classification
 theory of algebraic groups
 theory of algebraic geometry
 theory of theoretical physics
 
 | 
                        
                            
                                | gptkbp:class | gptkb:Lie_group 
 | 
                        
                            
                                | gptkbp:consistsOf | gptkb:G2 gptkb:F4
 E8
 E6
 E7
 
 | 
                        
                            
                                | gptkbp:namedFor | gptkb:Élie_Cartan 
 | 
                        
                            
                                | gptkbp:numberOfSimpleGroups | 5 
 | 
                        
                            
                                | gptkbp:relatedTo | gptkb:Weyl_group gptkb:geometry
 gptkb:symmetry
 gptkb:root
 gptkb:Cartan_classification
 gptkb:exceptional_Jordan_algebra
 gptkb:exceptional_Lie_algebra
 gptkb:octonions
 gptkb:exceptional_algebraic_groups
 gptkb:magic_square_(Lie_algebra)
 representation theory
 algebraic groups
 exceptional holonomy
 finite simple groups
 division algebras
 
 | 
                        
                            
                                | gptkbp:studiedBy | gptkb:mathematician physicists
 
 | 
                        
                            
                                | gptkbp:subclassOf | gptkb:Lie_group 
 | 
                        
                            
                                | gptkbp:usedIn | gptkb:grand_unified_theory gptkb:algebraic_geometry
 gptkb:theoretical_physics
 gptkb:string_theory
 differential geometry
 mathematical physics
 particle physics
 representation theory
 geometry of special holonomy
 octonionic geometry
 
 | 
                        
                            
                                | gptkbp:bfsParent | gptkb:Cayley_algebra gptkb:Albert_algebra
 gptkb:octonions
 
 | 
                        
                            
                                | gptkbp:bfsLayer | 6 
 | 
                        
                            
                                | https://www.w3.org/2000/01/rdf-schema#label | exceptional Lie groups 
 |