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gptkbp:instanceOf
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gptkb:Lie_group
|
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gptkbp:automorphismGroup
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gptkb:octonions
|
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gptkbp:Borel_subgroup
|
solvable subgroup
|
|
gptkbp:Cartan_matrix
|
[[2, -3], [-1, 2]]
|
|
gptkbp:centralTo
|
trivial
|
|
gptkbp:complexification
|
G2(C)
|
|
gptkbp:dimensions
|
14
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|
gptkbp:discoveredBy
|
gptkb:Wilhelm_Killing
gptkb:Élie_Cartan
|
|
gptkbp:discoveredIn
|
late 19th century
|
|
gptkbp:Dynkin_diagram
|
two nodes connected by a triple bond
|
|
gptkbp:fundamentalGroup
|
trivial (for compact form)
|
|
gptkbp:holonomy_group_of
|
7-dimensional Riemannian manifolds
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
exceptional Lie group G2
|
|
gptkbp:Lie_algebra
|
g2
|
|
gptkbp:maximal_compact_subgroup
|
SU(2) × SU(2)/Z2
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|
gptkbp:rank
|
2
|
|
gptkbp:realForm
|
compact
split
|
|
gptkbp:relatedTo
|
gptkb:F4
gptkb:exceptional_Jordan_algebra
gptkb:octonions
E8
E6
E7
subgroup of E6
subgroup of E7
subgroup of E8
subgroup of F4
subgroup of GL(7, R)
subgroup of SO(7)
subgroup of SO(8)
subgroup of Spin(7)
subgroup of Spin(8)
automorphisms of the octonion algebra
special holonomy in 7 dimensions
symmetries of the 7-sphere
symmetries of the Fano plane
|
|
gptkbp:type
|
gptkb:G2_root_system
|
|
gptkbp:used_in
|
gptkb:string_theory
gptkb:M-theory
differential geometry
theory of special holonomy
|
|
gptkbp:Weyl_group
|
gptkb:dihedral_group_of_order_12
12
|
|
gptkbp:bfsParent
|
gptkb:Lie_group
|
|
gptkbp:bfsLayer
|
5
|