E 6 Lie algebra

URI: https://gptkb.org/entity/E_6_Lie_algebra

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:Lie_group
gptkbp:automorphismGroup	gptkb:E_6_automorphism_group
gptkbp:Cartan_matrix	gptkb:E_6_Cartan_matrix
gptkbp:centralTo	trivial
gptkbp:dimensions	78
gptkbp:discoveredBy	gptkb:Élie_Cartan
gptkbp:Dynkin_diagram	gptkb:E_6_Dynkin_diagram
gptkbp:hasChevalleyBasis	yes
gptkbp:hasCompactForm	compact real form of E_6
gptkbp:hasConnection	false
gptkbp:hasFundamentalRepresentation	27-dimensional representation 351-dimensional representation 78-dimensional adjoint representation
gptkbp:hasKillingForm	non-degenerate
gptkbp:hasOrderOfWeylGroup	51840
gptkbp:hasOuterAutomorphism	order 2
gptkbp:hasRootLattice	gptkb:E_6_lattice
gptkbp:hasSubalgebra	gptkb:A_2_Lie_algebra gptkb:A_5_Lie_algebra gptkb:D_5_Lie_algebra gptkb:F_4_Lie_algebra
gptkbp:isSemisimple	true
gptkbp:isSimple	true
gptkbp:rank	6 complex numbers
gptkbp:realForm	gptkb:E_6(-14) gptkb:E_6(-26) gptkb:E_6(2) gptkb:E_6(6)
gptkbp:relatedGroup	gptkb:E_6_(mathematics)
gptkbp:relatedTo	gptkb:grand_unified_theory gptkb:string_theory gptkb:exceptional_Jordan_algebra gptkb:octonions
gptkbp:subclassOf	gptkb:E_7_Lie_algebra gptkb:E_8_Lie_algebra
gptkbp:type	gptkb:E_6_root_system gptkb:exceptional_Lie_algebra
gptkbp:usedIn	gptkb:algebraic_geometry gptkb:theoretical_physics representation theory string compactification grand unified models
gptkbp:Weyl_group	gptkb:E_6_Weyl_group
gptkbp:bfsParent	gptkb:E_6_Cartan_matrix gptkb:E_6_root_system
gptkbp:bfsLayer	9
https://www.w3.org/2000/01/rdf-schema#label	E 6 Lie algebra