|
gptkbp:instanceOf
|
gptkb:Lie_group
|
|
gptkbp:automorphismGroup
|
trivial
|
|
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:discoveredIn
|
late 19th century
|
|
gptkbp:Dynkin_diagram
|
gptkb:E8_Dynkin_diagram
|
|
gptkbp:field_of_definition
|
complex numbers
finite fields
real numbers
|
|
gptkbp:fundamentalGroup
|
trivial
|
|
gptkbp:Lie_algebra
|
gptkb:E8_Lie_algebra
|
|
gptkbp:notableFor
|
connected
simply connected
largest exceptional simple Lie group
no nontrivial center
no outer automorphisms
|
|
gptkbp:number_of_positive_roots
|
120
|
|
gptkbp:number_of_roots
|
240
|
|
gptkbp:number_of_simple_roots
|
8
|
|
gptkbp:quasi-split_real_form
|
E8(-24)
|
|
gptkbp:rank
|
8
|
|
gptkbp:realForm
|
3
|
|
gptkbp:relatedTo
|
gptkb:E8_lattice
gptkb:G2
gptkb:F4
gptkb:exceptional_Jordan_algebra
gptkb:octonions
gptkb:E8_polytope
gptkb:E8_manifold
E6
E7
exceptional Lie algebra E8
|
|
gptkbp:split_real_form
|
E8(8)
|
|
gptkbp:type
|
gptkb:E8_root_system
gptkb:Lie_group
|
|
gptkbp:usedIn
|
gptkb:algebraic_geometry
gptkb:geometry
gptkb:mathematics
gptkb:theoretical_physics
gptkb:topology
gptkb:string_theory
representation theory
grand unified theories
|
|
gptkbp:Weyl_group
|
696729600
|
|
gptkbp:bfsParent
|
gptkb:E8_Dynkin_diagram
|
|
gptkbp:bfsLayer
|
8
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
exceptional Lie group E8
|