|
gptkbp:instanceOf
|
gptkb:Lie_group
|
|
gptkbp:automorphismGroup
|
cyclic group of order 2
|
|
gptkbp:centralTo
|
cyclic group of order 3
|
|
gptkbp:compact_real_form
|
E_6 (compact)
|
|
gptkbp:dimensions
|
78
|
|
gptkbp:discoveredBy
|
gptkb:Élie_Cartan
|
|
gptkbp:Dynkin_diagram
|
E6
|
|
gptkbp:field_of_definition
|
complex numbers
finite fields
real numbers
|
|
gptkbp:first_classified
|
1894
|
|
gptkbp:fundamentalGroup
|
cyclic group of order 3
|
|
gptkbp:has_maximal_torus
|
rank 6 torus
|
|
gptkbp:hasSubgroup
|
gptkb:SU(6)_×_SU(2)
gptkb:Spin(10)
gptkb:F_4_group
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
E 6 group
|
|
gptkbp:notation
|
gptkb:E_6
|
|
gptkbp:quaternionic_real_form
|
E_6 (2)
|
|
gptkbp:rank
|
6
|
|
gptkbp:realForm
|
3
|
|
gptkbp:relatedTo
|
gptkb:Weyl_group
gptkb:E_8_group
gptkb:Albert_algebra
gptkb:exceptional_Jordan_algebra
gptkb:Freudenthal_magic_square
gptkb:octonions
gptkb:E_7_group
gptkb:F_4_group
gptkb:G_2_group
Borel subgroup
Cartan matrix of E6
Lie algebra of type E6
root lattice of E6
weight lattice of E6
|
|
gptkbp:represents
|
78-dimensional adjoint representation
27-dimensional fundamental representation
|
|
gptkbp:split_real_form
|
E_6 (6)
|
|
gptkbp:type
|
gptkb:Lie_group
gptkb:E6_root_system
|
|
gptkbp:usedIn
|
gptkb:theoretical_physics
gptkb:string_theory
grand unified theories
|
|
gptkbp:Weyl_group
|
51840
|
|
gptkbp:bfsParent
|
gptkb:E_8_group
|
|
gptkbp:bfsLayer
|
8
|