Statements (25)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:characterizedBy |
having no nontrivial connected solvable normal subgroups
|
| gptkbp:class |
gptkb:Dynkin_diagrams
by root systems |
| gptkbp:definedIn |
gptkb:Lie_theory
|
| gptkbp:example |
gptkb:special_linear_group_SL(n,_R)
gptkb:special_orthogonal_group_SO(n) gptkb:symplectic_group_Sp(n) |
| https://www.w3.org/2000/01/rdf-schema#label |
semisimple Lie groups
|
| gptkbp:importantFor |
gptkb:theoretical_physics
differential geometry representation theory |
| gptkbp:property |
every compact semisimple Lie group is linear
finite center universal covering group is also semisimple finite-dimensional representations are completely reducible |
| gptkbp:relatedTo |
gptkb:semisimple_Lie_algebras
gptkb:simple_Lie_groups reductive Lie groups |
| gptkbp:studiedBy |
gptkb:Élie_Cartan
|
| gptkbp:subclassOf |
gptkb:Lie_group
|
| gptkbp:bfsParent |
gptkb:Lie_group
gptkb:Lie_groups gptkb:Kazhdan–Margulis_theorem |
| gptkbp:bfsLayer |
5
|