|
gptkbp:instanceOf
|
gptkb:Lie_group
|
|
gptkbp:automorphismGroup
|
trivial group
|
|
gptkbp:Bourbaki_label
|
gptkb:G2
|
|
gptkbp:Cartan_matrix
|
[[2, -3], [-1, 2]]
|
|
gptkbp:centralTo
|
trivial group
|
|
gptkbp:compact
|
G2 (compact real form)
|
|
gptkbp:dimensions
|
14
|
|
gptkbp:discoveredBy
|
gptkb:Élie_Cartan
|
|
gptkbp:Dynkin_diagram
|
gptkb:G2_Dynkin_diagram
|
|
gptkbp:fundamentalGroup
|
trivial group
|
|
gptkbp:has_14-dimensional_adjoint_representation
|
yes
|
|
gptkbp:has_7-dimensional_representation
|
yes
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
G2 (complex Lie group)
|
|
gptkbp:Lie_algebra
|
g2
|
|
gptkbp:number_of_positive_roots
|
6
|
|
gptkbp:number_of_roots
|
12
|
|
gptkbp:number_of_simple_roots
|
2
|
|
gptkbp:rank
|
2
|
|
gptkbp:realForm
|
G2 (real Lie group)
|
|
gptkbp:relatedTo
|
gptkb:exceptional_Jordan_algebra
gptkb:exceptional_Lie_algebra
gptkb:octonions
exceptional holonomy
Lie group classification
automorphism group of the octonions
|
|
gptkbp:split_form
|
G2 (split real form)
|
|
gptkbp:type
|
gptkb:Lie_group
gptkb:G2_root_system
|
|
gptkbp:Weyl_group
|
gptkb:dihedral_group_of_order_12
|
|
gptkbp:bfsParent
|
gptkb:G2_Lie_group
|
|
gptkbp:bfsLayer
|
7
|