|
gptkbp:instanceOf
|
gptkb:Lie_group
|
|
gptkbp:Cartan_matrix
|
[[2,-3],[-1,2]]
|
|
gptkbp:centralTo
|
trivial
|
|
gptkbp:compact_real_form
|
gptkb:automorphism_group_of_octonions
|
|
gptkbp:dimensions
|
14
|
|
gptkbp:discoveredBy
|
gptkb:Élie_Cartan
|
|
gptkbp:Dynkin_diagram
|
gptkb:Dynkin_diagram_of_G2
|
|
gptkbp:fundamentalGroup
|
trivial
|
|
gptkbp:hasChevalleyGroup
|
gptkb:G_2(q)
|
|
gptkbp:hasFundamentalWeights
|
2
|
|
gptkbp:hasIrreducibleRepresentation
|
14-dimensional (adjoint)
27-dimensional
7-dimensional
|
|
gptkbp:hasMaximalTorus
|
2-dimensional
|
|
gptkbp:hasRootLengths
|
long and short roots
|
|
gptkbp:hasSubgroup
|
gptkb:SO(7)
gptkb:Spin(7)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
G 2
|
|
gptkbp:Lie_algebra
|
g_2
|
|
gptkbp:rank
|
2
|
|
gptkbp:realForm
|
compact
split
|
|
gptkbp:relatedTo
|
gptkb:E_6
gptkb:E_7
gptkb:E_8
gptkb:exceptional_Jordan_algebra
gptkb:automorphism_group_of_octonions
gptkb:magic_square_(Freudenthal–Tits_construction)
gptkb:octonionic_projective_plane
gptkb:octonions
F_4
exceptional holonomy
special holonomy manifolds
|
|
gptkbp:split_real_form
|
split G_2
|
|
gptkbp:type
|
gptkb:Lie_group
gptkb:G2_root_system
|
|
gptkbp:usedIn
|
gptkb:string_theory
gptkb:M-theory
differential geometry
representation theory
algebraic groups
theory of calibrations
theory of special holonomy
|
|
gptkbp:Weyl_group
|
gptkb:dihedral_group_of_order_12
12
|
|
gptkbp:bfsParent
|
gptkb:Weyl_group
|
|
gptkbp:bfsLayer
|
5
|