|
gptkbp:instanceOf
|
gptkb:Lie_group
|
|
gptkbp:automorphismGroup
|
gptkb:E7_group
|
|
gptkbp:Cartan_matrix
|
gptkb:E7_Cartan_matrix
|
|
gptkbp:centralTo
|
trivial
|
|
gptkbp:class
|
gptkb:Cartan_classification
|
|
gptkbp:dimensions
|
133
|
|
gptkbp:discoveredBy
|
gptkb:Wilhelm_Killing
gptkb:Élie_Cartan
|
|
gptkbp:Dynkin_diagram
|
gptkb:E7_Dynkin_diagram
|
|
gptkbp:hasAdjointRepresentation
|
133-dimensional representation
|
|
gptkbp:hasBorelSubalgebra
|
yes
|
|
gptkbp:hasCartanSubalgebra
|
7-dimensional
|
|
gptkbp:hasChevalleyBasis
|
yes
|
|
gptkbp:hasConnection
|
false
|
|
gptkbp:hasFundamentalRepresentation
|
56-dimensional representation
|
|
gptkbp:hasKillingForm
|
non-degenerate
|
|
gptkbp:hasOuterAutomorphism
|
trivial
|
|
gptkbp:hasParabolicSubalgebra
|
yes
|
|
gptkbp:hasRootLattice
|
gptkb:E7_lattice
|
|
gptkbp:hasWeightLattice
|
gptkb:E7_weight_lattice
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
E7 Lie algebra
|
|
gptkbp:isCenterless
|
true
|
|
gptkbp:isCompactForm
|
gptkb:E7(-133)
|
|
gptkbp:isSemisimple
|
true
|
|
gptkbp:isSimple
|
true
|
|
gptkbp:isSplitForm
|
E7(7)
|
|
gptkbp:rank
|
7
complex numbers
|
|
gptkbp:realForm
|
gptkb:E7(-133)
E7(7)
E7(-25)
E7(-5)
|
|
gptkbp:relatedTo
|
gptkb:E6_Lie_algebra
gptkb:G2_Lie_algebra
gptkb:E8_Lie_algebra
gptkb:exceptional_Lie_groups
gptkb:F4_Lie_algebra
gptkb:E7_group
|
|
gptkbp:type
|
gptkb:exceptional_Lie_algebra
gptkb:E7_root_system
|
|
gptkbp:usedIn
|
gptkb:algebraic_geometry
gptkb:theoretical_physics
gptkb:string_theory
gptkb:supergravity
representation theory
algebraic groups
|
|
gptkbp:Weyl_group
|
gptkb:E7_Weyl_group
|
|
gptkbp:bfsParent
|
gptkb:E7(q)
gptkb:exceptional_Lie_group_E7
|
|
gptkbp:bfsLayer
|
6
|