|
gptkbp:instanceOf
|
gptkb:Lie_group
|
|
gptkbp:automorphismGroup
|
gptkb:G2_group
|
|
gptkbp:Cartan_matrix
|
[[2,-3],[-1,2]]
|
|
gptkbp:centralTo
|
trivial
|
|
gptkbp:compact_real_form
|
gptkb:automorphism_group_of_octonions
|
|
gptkbp:complexification
|
G2(C)
|
|
gptkbp:dimensions
|
14
|
|
gptkbp:discoveredBy
|
gptkb:Élie_Cartan
|
|
gptkbp:discoveredIn
|
1894
|
|
gptkbp:Dynkin_diagram
|
two nodes connected by a triple bond
|
|
gptkbp:field
|
complex numbers
finite fields
real numbers
|
|
gptkbp:fundamentalGroup
|
trivial
|
|
gptkbp:hasMaximalSubgroup
|
gptkb:SU(3)
gptkb:SL(3,R)
SO(4)
SL(2,R)×SL(2,R)
|
|
gptkbp:hasSubgroup
|
gptkb:SO(7)
gptkb:Spin(7)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
G2 group
|
|
gptkbp:Lie_algebra
|
g2
|
|
gptkbp:rank
|
2
|
|
gptkbp:realForm
|
compact form
split form
|
|
gptkbp:relatedTo
|
gptkb:Weyl_group
gptkb:algebraic_geometry
gptkb:geometry
gptkb:string_theory
gptkb:exceptional_Jordan_algebra
gptkb:M-theory
gptkb:exceptional_Lie_algebra
gptkb:octonions
differential geometry
group theory
mathematical physics
representation theory
exceptional holonomy
special holonomy
G2 manifold
octonion automorphisms
|
|
gptkbp:split_real_form
|
split G2
|
|
gptkbp:type
|
gptkb:G2_root_system
|
|
gptkbp:Weyl_group
|
gptkb:dihedral_group_of_order_12
|
|
gptkbp:bfsParent
|
gptkb:Cayley_numbers
|
|
gptkbp:bfsLayer
|
7
|