Statements (28)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:automorphismGroup |
gptkb:G_2_group
|
| gptkbp:Cartan_matrix |
[[2, -3], [-1, 2]]
|
| gptkbp:centralTo |
trivial
|
| gptkbp:class |
one of five exceptional simple Lie algebras
|
| gptkbp:dimensions |
14
|
| gptkbp:discoveredBy |
gptkb:Wilhelm_Killing
|
| gptkbp:Dynkin_diagram |
two nodes, one triple bond
|
| gptkbp:fundamental_representations |
14-dimensional (adjoint)
7-dimensional |
| gptkbp:highest_root |
long root
|
| https://www.w3.org/2000/01/rdf-schema#label |
G 2 Lie algebra
|
| gptkbp:long_roots |
6
|
| gptkbp:rank |
2
|
| gptkbp:realForm |
compact real form
split real form |
| gptkbp:relatedTo |
gptkb:octonions
gptkb:exceptional_Lie_group_G_2 |
| gptkbp:short_roots |
6
|
| gptkbp:type |
gptkb:exceptional_Lie_algebra
gptkb:G_2_root_system |
| gptkbp:used_in |
gptkb:string_theory
differential geometry theory of special holonomy |
| gptkbp:Weyl_group |
12
|
| gptkbp:bfsParent |
gptkb:G_2(q)
gptkb:D_n_Lie_algebra |
| gptkbp:bfsLayer |
7
|