root system E8

URI: https://gptkb.org/entity/root_system_E8
GPTKB entity
Statements (28)
Predicate Object
gptkbp:instanceOf gptkb:root
gptkbp:all_roots_have_same_length true
gptkbp:dimension_of_ambient_space 8
gptkbp:discoveredBy gptkb:Wilhelm_Killing
gptkbp:discoveredIn late 19th century
gptkbp:Dynkin_diagram E8
gptkbp:has_no_proper_subsystems_of_full_rank true
https://www.w3.org/2000/01/rdf-schema#label root system E8
gptkbp:is_associated_Lie_algebra gptkb:E8_Lie_algebra
gptkbp:is_associated_Lie_group gptkb:E8_Lie_group
gptkbp:is_crystallographic true
gptkbp:is_irreducible true
gptkbp:is_simply_laced true
gptkbp:number_of_roots 240
gptkbp:rank 8
gptkbp:related_lattice gptkb:E8_lattice
gptkbp:relatedTo gptkb:Gosset_polytope_4_21
gptkb:exceptional_Lie_groups
gptkb:octonions
gptkbp:type exceptional root system
gptkbp:used_in gptkb:Lie_theory
gptkb:algebraic_geometry
gptkb:theoretical_physics
gptkb:string_theory
gptkbp:Weyl_group 696729600
gptkbp:bfsParent gptkb:Aut(E8)
gptkb:E8_Dynkin_diagram
gptkbp:bfsLayer 7