E 8 (mathematics)

URI: https://gptkb.org/entity/E_8_(mathematics)
GPTKB entity
Statements (48)
Predicate Object
gptkbp:instanceOf gptkb:Lie_group
gptkb:root
gptkbp:automorphismGroup gptkb:E_8_(mathematics)
gptkbp:Cartan_matrix gptkb:E_8_Cartan_matrix
gptkbp:centralTo trivial group
gptkbp:compact true (for compact real form)
gptkbp:dimensions 248
gptkbp:discoveredBy gptkb:Wilhelm_Killing
gptkb:Élie_Cartan
gptkbp:Dynkin_diagram gptkb:E_8_Dynkin_diagram
gptkbp:fundamentalGroup trivial group
gptkbp:hasConnection true
gptkbp:hasCoxeterNumber 30
gptkbp:hasDualCoxeterNumber 30
gptkbp:hasExponents 1, 7, 11, 13, 17, 19, 23, 29
gptkbp:hasFundamentalRepresentation adjoint representation
gptkbp:hasFundamentalRepresentationDimension 248
gptkbp:hasHighestRoot gptkb:E_8_highest_root
gptkbp:hasNoOuterAutomorphisms true
gptkbp:hasRootLattice gptkb:E_8_lattice
gptkbp:hasRootNumber 240
gptkbp:hasSmallestNontrivialRepresentationDimension 248
gptkbp:hasWeightLattice gptkb:E_8_weight_lattice
gptkbp:hasWeylGroupOrder 696729600
https://www.w3.org/2000/01/rdf-schema#label E 8 (mathematics)
gptkbp:isComplex true
gptkbp:isExceptional true
gptkbp:isSimple true
gptkbp:isSplit true (for split real form)
gptkbp:partOf gptkb:exceptional_Lie_groups
gptkb:E_series
gptkbp:rank 8
gptkbp:realForm compact real form
split real form
gptkbp:relatedTo gptkb:E_8_Weyl_group
gptkb:E_8_lattice
gptkb:E_8_manifold
gptkb:E_8_polytope
gptkb:E_8_root_system
gptkbp:type gptkb:Lie_group
complex Lie algebra
gptkbp:usedIn gptkb:algebraic_geometry
gptkb:theoretical_physics
gptkb:string_theory
mathematical physics
representation theory
gptkbp:bfsParent gptkb:E_8_Lie_algebra
gptkbp:bfsLayer 7