Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:application |
differential geometry
particle physics representation theory |
| gptkbp:characterizedBy |
no nontrivial connected normal subgroups
|
| gptkbp:class |
gptkb:Cartan_classification
gptkb:Dynkin_diagrams A_n, B_n, C_n, D_n, E_6, E_7, E_8, F_4, G_2 types |
| gptkbp:finiteCover |
simply connected simple Lie group
|
| gptkbp:includes |
gptkb:exceptional_Lie_groups
gptkb:special_orthogonal_group_SO(n) gptkb:symplectic_group_Sp(n) gptkb:special_linear_group_SL(n,R) |
| gptkbp:namedAfter |
gptkb:Sophus_Lie
|
| gptkbp:property |
connected
non-abelian (except for one-dimensional case) |
| gptkbp:relatedTo |
gptkb:Lie_algebras
gptkb:semisimple_Lie_groups |
| gptkbp:studiedIn |
gptkb:mathematics
gptkb:theoretical_physics |
| gptkbp:subclassOf |
gptkb:Lie_group
gptkb:simple_group |
| gptkbp:usedIn |
gptkb:gauge_theory
gptkb:Standard_Model_of_particle_physics |
| gptkbp:bfsParent |
gptkb:Lie_groups
|
| gptkbp:bfsLayer |
6
|
| https://www.w3.org/2000/01/rdf-schema#label |
simple Lie groups
|