E8 root system

URI: https://gptkb.org/entity/E8_root_system

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:root
gptkbp:automorphismGroup	gptkb:Weyl_group_of_E8
gptkbp:dimension_of_ambient_space	8
gptkbp:discoveredBy	gptkb:Wilhelm_Killing
gptkbp:discoveredIn	1887
gptkbp:Dynkin_diagram	gptkb:E8_Dynkin_diagram
gptkbp:has_Coxeter_number	30
gptkbp:has_dual_Coxeter_number	30
gptkbp:has_exponents	1, 7, 11, 13, 17, 19, 23, 29
https://www.w3.org/2000/01/rdf-schema#label	E8 root system
gptkbp:is_crystallographic	true
gptkbp:is_even	true
gptkbp:is_even_unimodular_lattice	true
gptkbp:is_irreducible	true
gptkbp:is_self-dual	true
gptkbp:is_simply_laced	true
gptkbp:is_unimodular	true
gptkbp:Lie_algebra	gptkb:E8_Lie_algebra
gptkbp:number_of_roots	240
gptkbp:rank	8
gptkbp:related_lattice	gptkb:E8_lattice
gptkbp:relatedTo	gptkb:Gosset_4_21_polytope gptkb:Niemeier_lattices gptkb:string_theory gptkb:exceptional_Lie_groups gptkb:Leech_lattice gptkb:octonions gptkb:Monstrous_Moonshine gptkb:E8_polytope gptkb:Borcherds'_theory gptkb:E8_manifold modular forms string theory compactification
gptkbp:used_in	gptkb:Lie_theory gptkb:theoretical_physics gptkb:string_theory coding theory sphere packing
gptkbp:Weyl_group	696729600
gptkbp:bfsParent	gptkb:E8(q) gptkb:exceptional_Lie_group_E8
gptkbp:bfsLayer	6