|
gptkbp:instanceOf
|
gptkb:Lie_group
|
|
gptkbp:automorphismGroup
|
inner automorphisms only
|
|
gptkbp:Cartan_matrix
|
E8 Cartan matrix
|
|
gptkbp:centralTo
|
trivial
|
|
gptkbp:compact_real_form
|
E8
|
|
gptkbp:dimensions
|
248
|
|
gptkbp:discoveredBy
|
gptkb:Wilhelm_Killing
gptkb:Élie_Cartan
|
|
gptkbp:Dynkin_diagram
|
gptkb:E8_Dynkin_diagram
|
|
gptkbp:formsComplexWith
|
E8(C)
|
|
gptkbp:fundamentalGroup
|
trivial
|
|
gptkbp:has_Coxeter_number
|
30
|
|
gptkbp:has_dual_Coxeter_number
|
30
|
|
gptkbp:has_fundamental_weights
|
8
|
|
gptkbp:has_highest_root
|
theta
|
|
gptkbp:has_Killing_form
|
non-degenerate
|
|
gptkbp:has_maximal_torus
|
8-dimensional
|
|
gptkbp:has_no_outer_automorphisms
|
true
|
|
gptkbp:has_root_lattice
|
gptkb:E8_lattice
|
|
gptkbp:has_trivial_center
|
true
|
|
gptkbp:has_trivial_fundamental_group
|
true
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
E8 group
|
|
gptkbp:Lie_algebra
|
gptkb:E8_Lie_algebra
|
|
gptkbp:rank
|
8
|
|
gptkbp:realForm
|
3
|
|
gptkbp:relatedTo
|
gptkb:algebraic_geometry
gptkb:E8_lattice
gptkb:Gosset_polytope_4_21
gptkb:string_theory
gptkb:exceptional_Lie_algebras
gptkb:octonions
gptkb:Lie_algebra_E8
mathematical physics
grand unified theory
unimodular lattice
Bourbaki group naming
|
|
gptkbp:split_real_form
|
E8(8)
|
|
gptkbp:type
|
gptkb:E8_root_system
gptkb:Lie_group
|
|
gptkbp:used_in
|
gptkb:algebraic_geometry
gptkb:theoretical_physics
representation theory
grand unified theories
string theory models
|
|
gptkbp:Weyl_group
|
696729600
|
|
gptkbp:bfsParent
|
gptkb:E8×E8_heterotic_string
|
|
gptkbp:bfsLayer
|
6
|