|
gptkbp:instanceOf
|
gptkb:Lie_group
|
|
gptkbp:adjoint_representation_dimension
|
14
|
|
gptkbp:automorphismGroup
|
adjoint group of type G_2
|
|
gptkbp:Cartan_matrix
|
[[2,-3],[-1,2]]
|
|
gptkbp:Cartan_subalgebra_dimension
|
2
|
|
gptkbp:centralTo
|
trivial
|
|
gptkbp:class
|
gptkb:exceptional_Lie_algebra
|
|
gptkbp:dimensions
|
14
|
|
gptkbp:discoveredBy
|
gptkb:Wilhelm_Killing
|
|
gptkbp:Dynkin_diagram
|
two nodes, one triple bond
|
|
gptkbp:fundamental_representations
|
7-dimensional
14-dimensional
|
|
gptkbp:highest_root
|
long root
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Lie algebra of type G 2
|
|
gptkbp:Killing_form
|
non-degenerate
|
|
gptkbp:long_roots
|
6
|
|
gptkbp:rank
|
2
complex numbers
|
|
gptkbp:realForm
|
compact real form
split real form
|
|
gptkbp:related_to_octonions
|
true
|
|
gptkbp:relatedGroup
|
G_2 (Lie group)
|
|
gptkbp:short_roots
|
6
|
|
gptkbp:smallest_exceptional_Lie_algebra
|
true
|
|
gptkbp:structure_constants
|
defined by G_2 root system
|
|
gptkbp:subalgebra_of
|
gptkb:so(7)
|
|
gptkbp:type
|
gptkb:G_2_root_system
|
|
gptkbp:used_in
|
gptkb:string_theory
differential geometry
exceptional holonomy
theory of octonions
|
|
gptkbp:Weyl_group
|
12
|
|
gptkbp:bfsParent
|
gptkb:root_system_G_2
|
|
gptkbp:bfsLayer
|
8
|