|
gptkbp:instanceOf
|
gptkb:Lie_group
|
|
gptkbp:automorphismGroup
|
gptkb:Z/2Z
E6 (adjoint group)
|
|
gptkbp:Cartan_matrix
|
gptkb:E6_Cartan_matrix
|
|
gptkbp:centralTo
|
trivial
|
|
gptkbp:compact_real_form
|
yes
|
|
gptkbp:dimensions
|
78
|
|
gptkbp:discoveredBy
|
gptkb:Élie_Cartan
|
|
gptkbp:discoveredIn
|
1894
|
|
gptkbp:Dynkin_diagram
|
E6
|
|
gptkbp:fundamental_representations
|
27-dimensional
351-dimensional
78-dimensional (adjoint)
|
|
gptkbp:has_outer_automorphism
|
yes
|
|
gptkbp:has_triality
|
no
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Lie algebra E6
|
|
gptkbp:isomorphicTo
|
no other simple Lie algebra
|
|
gptkbp:rank
|
6
complex numbers
|
|
gptkbp:realForm
|
3
|
|
gptkbp:relatedGroup
|
gptkb:E6_(Lie_group)
E6 (adjoint group)
E6 (simply connected group)
|
|
gptkbp:relatedTo
|
gptkb:Albert_algebra
gptkb:exceptional_Jordan_algebra
gptkb:Freudenthal_magic_square
gptkb:octonions
exceptional groups
GUT models
symmetry in string theory
|
|
gptkbp:root_lattice
|
E6 lattice
|
|
gptkbp:split_real_form
|
yes
|
|
gptkbp:subalgebra
|
gptkb:F4
so(10)
su(3) + su(3) + su(3)
su(6) + su(2)
|
|
gptkbp:type
|
gptkb:exceptional_Lie_algebra
E6
|
|
gptkbp:used_in
|
gptkb:theoretical_physics
gptkb:string_theory
grand unified theories
|
|
gptkbp:Weyl_group
|
51840
|
|
gptkbp:bfsParent
|
gptkb:E6_(Lie_group)
|
|
gptkbp:bfsLayer
|
7
|