E 8 (Lie group)

URI: https://gptkb.org/entity/E_8_(Lie_group)

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:Lie_group
gptkbp:automorphismGroup	trivial
gptkbp:Cartan_matrix	gptkb:E_8_Cartan_matrix
gptkbp:centralTo	trivial
gptkbp:compact_real_form	gptkb:E_8
gptkbp:dimensions	248
gptkbp:discoveredBy	gptkb:Wilhelm_Killing
gptkbp:discoveredIn	1894
gptkbp:Dynkin_diagram	gptkb:E_8_Dynkin_diagram
gptkbp:field_of_definition	complex numbers finite fields real numbers
gptkbp:fundamentalGroup	trivial
gptkbp:rank	8
gptkbp:realForm	3
gptkbp:related_algebra	gptkb:E_8_Lie_algebra
gptkbp:relatedTo	gptkb:grand_unified_theory gptkb:E_8_singularity gptkb:string_theory gptkb:Bourbaki_group gptkb:E_8_lattice gptkb:E_8_manifold gptkb:E_8_polytope gptkb:exceptional_Lie_algebras gptkb:octonions Lie algebra classification exceptional groups E-series Lie groups E_6 (Lie group) E_7 (Lie group) F_4 (Lie group) G_2 (Lie group)
gptkbp:split_real_form	E_8(8)
gptkbp:studiedBy	gptkb:Élie_Cartan
gptkbp:type	gptkb:Lie_group gptkb:E_8_root_system
gptkbp:used_in	gptkb:algebraic_geometry gptkb:theoretical_physics gptkb:string_theory mathematical physics representation theory grand unified theories
gptkbp:Weyl_group	696729600
gptkbp:bfsParent	gptkb:E_8_(compact_real_form)
gptkbp:bfsLayer	10
https://www.w3.org/2000/01/rdf-schema#label	E 8 (Lie group)