E6 Lie algebra

URI: https://gptkb.org/entity/E6_Lie_algebra

GPTKB entity

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
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:E8_Lie_algebra gptkb:E6_Lie_group
gptkbp:bfsLayer	8
https://www.w3.org/2000/01/rdf-schema#label	E6 Lie algebra