E6 Lie algebra

URI: https://gptkb.org/entity/E6_Lie_algebra
GPTKB entity
Statements (36)
Predicate Object
gptkbp:instanceOf gptkb:Lie_group
gptkbp:automorphismGroup gptkb:Z/2Z
gptkbp:Cartan_matrix gptkb:E6_Cartan_matrix
gptkbp:centralTo trivial
gptkbp:dimensions 78
gptkbp:discoveredBy gptkb:Wilhelm_Killing
gptkb:Élie_Cartan
gptkbp:Dynkin_diagram E6
gptkbp:first_classified late 19th century
gptkbp:fundamental_representation 27-dimensional
351-dimensional
78-dimensional adjoint
gptkbp:has_real_forms compact real form
split real form
Hermitian symmetric real form
https://www.w3.org/2000/01/rdf-schema#label E6 Lie algebra
gptkbp:rank 6
complex numbers
gptkbp:relatedGroup gptkb:E6_Lie_group
gptkbp:relatedTo gptkb:E7_Lie_algebra
gptkb:E8_Lie_algebra
gptkb:exceptional_Jordan_algebra
gptkb:octonions
gptkb:F4_Lie_algebra
gptkb:D5_Lie_algebra
gptkbp:type gptkb:exceptional_Lie_algebra
gptkb:E6_root_system
gptkbp:used_in gptkb:theoretical_physics
gptkb:string_theory
grand unified theories
gptkbp:Weyl_group 51840
gptkbp:bfsParent gptkb:E7_Lie_algebra
gptkb:E8_Lie_algebra
gptkb:E6_diagram
gptkb:E6_root_system
gptkbp:bfsLayer 7