Lie algebra E8

URI: https://gptkb.org/entity/Lie_algebra_E8
GPTKB entity
Statements (40)
Predicate Object
gptkbp:instanceOf gptkb:Lie_group
gptkbp:automorphismGroup E8 (adjoint group)
gptkbp:Cartan_matrix E8 Cartan matrix
gptkbp:centralTo trivial
gptkbp:class gptkb:Élie_Cartan
gptkbp:dimensions 248
gptkbp:discoveredBy gptkb:Wilhelm_Killing
gptkbp:Dynkin_diagram gptkb:E8_Dynkin_diagram
https://www.w3.org/2000/01/rdf-schema#label Lie algebra E8
gptkbp:rank 8
complex numbers
gptkbp:realForm E8(-24)
E8(8)
E8(-248)
gptkbp:relatedGroup E8 (mathematics)
gptkbp:relatedTo gptkb:E8_lattice
gptkb:Gosset_polytope_4_21
gptkb:string_theory
gptkb:Borcherds_algebra
gptkb:octonions
gptkb:E8×E8_heterotic_string
mathematical physics
modular forms
representation theory
algebraic groups
lattice theory
sphere packing
exceptional holonomy
finite simple groups
exceptional groups
gptkbp:type gptkb:E8_root_system
gptkb:Lie_group
gptkb:exceptional_Lie_algebra
gptkbp:used_in gptkb:theoretical_physics
gptkb:string_theory
grand unified theories
gptkbp:Weyl_group 696729600
gptkbp:bfsParent gptkb:Aut(E8)
gptkb:E8_group
gptkbp:bfsLayer 7