|
gptkbp:instanceOf
|
gptkb:Lie_group
|
|
gptkbp:acts_as_automorphisms_of
|
gptkb:octonion_algebra
|
|
gptkbp:actsOn
|
7-dimensional real vector space
|
|
gptkbp:automorphismGroup
|
gptkb:octonions
|
|
gptkbp:centralTo
|
trivial
|
|
gptkbp:compact_real_form
|
gptkb:G2
|
|
gptkbp:complexification
|
G2(C)
|
|
gptkbp:dimensions
|
14
|
|
gptkbp:discoveredBy
|
gptkb:Wilhelm_Killing
gptkb:Élie_Cartan
|
|
gptkbp:discoveredIn
|
late 19th century
|
|
gptkbp:Dynkin_diagram
|
gptkb:G2_Dynkin_diagram
|
|
gptkbp:fundamentalGroup
|
trivial
|
|
gptkbp:has_adjoint_representation_of_dimension
|
14
|
|
gptkbp:has_fundamental_representation_of_dimension
|
7
|
|
gptkbp:has_maximal_torus_of_dimension
|
2
|
|
gptkbp:hasSubgroup
|
gptkb:SO(7)
gptkb:Spin(7)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Lie group G2
|
|
gptkbp:Lie_algebra
|
g2
|
|
gptkbp:rank
|
2
|
|
gptkbp:realForm
|
compact
split
|
|
gptkbp:relatedTo
|
gptkb:Weyl_group
gptkb:holonomy_group
gptkb:string_theory
gptkb:exceptional_Jordan_algebra
gptkb:F4_(Lie_group)
gptkb:M-theory
gptkb:exceptional_Lie_algebra
gptkb:octonions
gptkb:magic_square_(Lie_algebra)
gptkb:E6_(Lie_group)
gptkb:E8_(Lie_group)
differential geometry
representation theory
Cartan subalgebra
weight lattice
exceptional holonomy
special holonomy
7-dimensional manifolds
E7 (Lie group)
special Riemannian geometry
|
|
gptkbp:split_real_form
|
gptkb:G2(2)
|
|
gptkbp:type
|
gptkb:Lie_group
gptkb:G2_root_system
|
|
gptkbp:Weyl_group
|
gptkb:dihedral_group_of_order_12
12
|
|
gptkbp:bfsParent
|
gptkb:G2_manifolds
|
|
gptkbp:bfsLayer
|
7
|