E 8

URI: https://gptkb.org/entity/E_8

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	true
gptkbp:dimensions	248
gptkbp:discoveredBy	gptkb:Wilhelm_Killing gptkb:Élie_Cartan
gptkbp:Dynkin_diagram	gptkb:E_8_Dynkin_diagram
gptkbp:fundamentalGroup	trivial
gptkbp:hasComplexForm	complex simple Lie group
gptkbp:hasConnection	true
gptkbp:hasCoxeterNumber	30
gptkbp:hasDualCoxeterNumber	30
gptkbp:hasExponents	1, 7, 11, 13, 17, 19, 23, 29
gptkbp:hasMaximalSubgroup	gptkb:A_1_×_E_7 gptkb:A_2_×_E_6 gptkb:A_4_×_A_4 gptkb:A_8 gptkb:D_8 gptkb:G_2_×_F_4 A_2 × A_2 × A_2 × A_2 A_5 × A_2 × A_1 E_7 × A_1
gptkbp:hasRootLattice	gptkb:E_8_lattice
gptkbp:hasWeylGroupOrder	696729600
https://www.w3.org/2000/01/rdf-schema#label	E 8
gptkbp:isSimple	true
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_Lie_algebra gptkb:E_8_gauge_theory gptkb:E_8_lattice gptkb:E_8_manifold gptkb:E_8_polytope
gptkbp:type	gptkb:Lie_group gptkb:E_8_root_system
gptkbp:usedIn	gptkb:theoretical_physics gptkb:string_theory grand unified theory
gptkbp:bfsParent	gptkb:Weyl_group
gptkbp:bfsLayer	5