|
gptkbp:instanceOf
|
gptkb:Lie_group
|
|
gptkbp:automorphismGroup
|
trivial
|
|
gptkbp:Cartan_matrix
|
E8 Cartan matrix
|
|
gptkbp:centralTo
|
trivial
|
|
gptkbp:compact
|
true (for compact real form)
|
|
gptkbp:complexification
|
real E8 Lie algebra
|
|
gptkbp:dimensions
|
248
|
|
gptkbp:discoveredBy
|
gptkb:Wilhelm_Killing
gptkb:Élie_Cartan
|
|
gptkbp:discoveredIn
|
late 19th century
|
|
gptkbp:Dynkin_diagram
|
gptkb:E8_Dynkin_diagram
|
|
gptkbp:hasChevalleyBasis
|
yes
|
|
gptkbp:hasConnection
|
true
|
|
gptkbp:hasSubalgebra
|
gptkb:E6_Lie_algebra
gptkb:E7_Lie_algebra
gptkb:G2_Lie_algebra
gptkb:F4_Lie_algebra
A1 Lie algebra
A8 Lie algebra
D8 Lie algebra
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
E8 Lie algebra
|
|
gptkbp:isCompactForm
|
yes (for compact real form)
|
|
gptkbp:isExceptional
|
true
|
|
gptkbp:isSemisimple
|
true
|
|
gptkbp:isSimple
|
true
|
|
gptkbp:isSplitForm
|
yes (for split real form)
|
|
gptkbp:numberOfPositiveRoots
|
120
|
|
gptkbp:numberOfRoots
|
240
|
|
gptkbp:rank
|
8
complex numbers
|
|
gptkbp:realForm
|
gptkb:E8_group
compact real form
split real form
|
|
gptkbp:relatedTo
|
gptkb:algebraic_geometry
gptkb:string_theory
gptkb:exceptional_Lie_groups
gptkb:E8_group
mathematical physics
representation theory
|
|
gptkbp:type
|
gptkb:E8_root_system
gptkb:exceptional_Lie_algebra
|
|
gptkbp:usedIn
|
gptkb:mathematics
gptkb:theoretical_physics
gptkb:Grand_Unified_Theories
|
|
gptkbp:Weyl_group
|
gptkb:E8_Weyl_group
|
|
gptkbp:bfsParent
|
gptkb:E8_lattice
gptkb:exceptional_Lie_group_E8
|
|
gptkbp:bfsLayer
|
6
|