|
gptkbp:instanceOf
|
gptkb:Lie_group
|
|
gptkbp:automorphismGroup
|
gptkb:G2_(Lie_group)
|
|
gptkbp:Cartan_matrix
|
gptkb:G2
|
|
gptkbp:centralTo
|
trivial
|
|
gptkbp:compact
|
yes (for compact real form)
|
|
gptkbp:dimensions
|
14
|
|
gptkbp:discoveredBy
|
gptkb:Wilhelm_Killing
gptkb:Élie_Cartan
|
|
gptkbp:discoveredIn
|
late 19th century
|
|
gptkbp:Dynkin_diagram
|
gptkb:Dynkin_diagram_of_type_G2
|
|
gptkbp:hasChevalleyBasis
|
yes
|
|
gptkbp:hasFundamentalRepresentation
|
14-dimensional (adjoint)
7-dimensional
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
G2 Lie algebra
|
|
gptkbp:isExceptional
|
true
|
|
gptkbp:isSimple
|
true
|
|
gptkbp:isSplit
|
yes (for split real form)
|
|
gptkbp:rank
|
2
|
|
gptkbp:realForm
|
compact real form
split real form
|
|
gptkbp:relatedGroup
|
gptkb:G2_(Lie_group)
|
|
gptkbp:relatedTo
|
gptkb:string_theory
gptkb:exceptional_Lie_algebras
gptkb:octonions
differential geometry
exceptional holonomy
|
|
gptkbp:subclassOf
|
gptkb:so(7)
octonion derivations
|
|
gptkbp:type
|
gptkb:G2_root_system
|
|
gptkbp:Weyl_group
|
gptkb:dihedral_group_of_order_12
|
|
gptkbp:bfsParent
|
gptkb:E7_Lie_algebra
gptkb:E8_Lie_algebra
gptkb:Dynkin_diagram_of_G2
gptkb:G2_root_system
|
|
gptkbp:bfsLayer
|
7
|