|
gptkbp:instanceOf
|
gptkb:Lie_group
|
|
gptkbp:automorphismGroup
|
gptkb:Z/2Z
|
|
gptkbp:Cartan_matrix
|
gptkb:E6_Cartan_matrix
|
|
gptkbp:centralTo
|
trivial
|
|
gptkbp:class
|
gptkb:Élie_Cartan
|
|
gptkbp:dimensions
|
78
|
|
gptkbp:discoveredBy
|
gptkb:Wilhelm_Killing
|
|
gptkbp:Dynkin_diagram
|
E6 Dynkin diagram
|
|
gptkbp:fundamental_representation
|
27-dimensional
351-dimensional
78-dimensional (adjoint)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Lie algebra E 6
|
|
gptkbp:maximal_compact_subgroup
|
gptkb:SU(6)_×_SU(2)
USp(8)
|
|
gptkbp:over_complex_numbers
|
unique up to isomorphism
|
|
gptkbp:rank
|
6
|
|
gptkbp:realForm
|
compact real form
split real form
Hermitian symmetric real form
|
|
gptkbp:relatedGroup
|
gptkb:E6_(Lie_group)
E6 (algebraic group)
|
|
gptkbp:relatedTo
|
gptkb:G2
gptkb:F4
gptkb:exceptional_Jordan_algebra
gptkb:Freudenthal_magic_square
gptkb:octonions
E8
E7
Deligne's exceptional series
|
|
gptkbp:subalgebra
|
gptkb:F4
so(10)
su(6) + su(2)
|
|
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:E_6_Lie_group
gptkb:E_6_singularity
|
|
gptkbp:bfsLayer
|
8
|