E 6 Lie group

URI: https://gptkb.org/entity/E_6_Lie_group

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:Lie_group
gptkbp:adjoint_representation_dimension	78
gptkbp:automorphismGroup	cyclic group of order 2
gptkbp:Cartan_matrix	gptkb:E6_Cartan_matrix
gptkbp:centralTo	cyclic group of order 3
gptkbp:compact	gptkb:compact_E_6
gptkbp:dimensions	78
gptkbp:discoveredBy	gptkb:Élie_Cartan
gptkbp:Dynkin_diagram	E6
gptkbp:fundamentalGroup	cyclic group of order 3
gptkbp:rank	6
gptkbp:realForm	gptkb:E_{6(-14)} gptkb:E_{6(-26)} gptkb:compact_E_6 gptkb:split_E_6 4
gptkbp:relatedGroup	gptkb:E_6_Lie_algebra gptkb:E_8_Lie_group gptkb:E_6_algebraic_group gptkb:E_6_finite_group gptkb:E_7_Lie_group gptkb:F_4_Lie_group gptkb:G_2_Lie_group
gptkbp:relatedTo	gptkb:Weyl_group gptkb:algebraic_geometry gptkb:theoretical_physics gptkb:Tits_construction gptkb:symmetry gptkb:Albert_algebra gptkb:exceptional_Jordan_algebra gptkb:Freudenthal_magic_square gptkb:octonions gptkb:Lie_algebra_E_6 mathematical physics representation theory exceptional groups
gptkbp:smallest_faithful_representation	27-dimensional
gptkbp:split_form	gptkb:split_E_6
gptkbp:type	gptkb:Lie_group gptkb:E6_root_system
gptkbp:used_in	gptkb:grand_unified_theory gptkb:string_theory
gptkbp:Weyl_group	51840
gptkbp:bfsParent	gptkb:E_6_root_system
gptkbp:bfsLayer	9
https://www.w3.org/2000/01/rdf-schema#label	E 6 Lie group