|
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
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
E 6 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:string_theory
gptkb:exceptional_Jordan_algebra
gptkb:octonions
grand unified theory
|
|
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
gptkb:D_n_Lie_algebra
|
|
gptkbp:bfsLayer
|
7
|