|
gptkbp:instanceOf
|
gptkb:Lie_group
|
|
gptkbp:adjoint_representation_dimension
|
248
|
|
gptkbp:automorphismGroup
|
trivial
|
|
gptkbp:Cartan_matrix
|
gptkb:E_8_Cartan_matrix
|
|
gptkbp:centralTo
|
trivial
|
|
gptkbp:compact
|
compact E_8
|
|
gptkbp:dimensions
|
248
|
|
gptkbp:discoveredBy
|
gptkb:Wilhelm_Killing
gptkb:Élie_Cartan
|
|
gptkbp:discoveredIn
|
1894
|
|
gptkbp:Dynkin_diagram
|
gptkb:E_8_Dynkin_diagram
|
|
gptkbp:fundamentalGroup
|
trivial
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
E 8 (complex Lie group)
|
|
gptkbp:Lie_algebra
|
gptkb:E_8_(Lie_algebra)
|
|
gptkbp:rank
|
8
|
|
gptkbp:realForm
|
E_8(-24)
E_8(-248)
E_8(8)
|
|
gptkbp:relatedTo
|
gptkb:Bott_periodicity
gptkb:algebraic_geometry
gptkb:topology
gptkb:Chevalley_groups
gptkb:string_theory
gptkb:Lie_algebra_cohomology
gptkb:exceptional_Jordan_algebra
gptkb:E_8_gauge_theory
gptkb:E_8_lattice
gptkb:E_8_manifold
gptkb:maximal_torus
gptkb:octonions
modular forms
representation theory
algebraic groups
homotopy theory
Borel subgroup
finite simple groups
Borel–de Siebenthal theory
|
|
gptkbp:smallest_faithful_representation
|
adjoint representation
|
|
gptkbp:split_form
|
split E_8
|
|
gptkbp:type
|
gptkb:Lie_group
gptkb:E_8_root_system
simply connected Lie group
|
|
gptkbp:used_in
|
gptkb:mathematics
gptkb:theoretical_physics
gptkb:string_theory
grand unified theories
|
|
gptkbp:Weyl_group
|
696729600
|
|
gptkbp:bfsParent
|
gptkb:E_8_(compact_real_form)
gptkb:E_8_(split_real_form)
|
|
gptkbp:bfsLayer
|
8
|