Statements (30)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
gptkb:Lie_group |
| gptkbp:basisFor |
Cartan subalgebra
|
| gptkbp:characterizedBy |
direct sum of simple Lie algebras
no nonzero solvable ideals |
| gptkbp:class |
gptkb:Weyl_group
gptkb:Cartan_classification |
| gptkbp:definedIn |
gptkb:Field
|
| gptkbp:example |
gptkb:sl(n,C)
so(n,C) exceptional Lie algebras (G2, F4, E6, E7, E8) sp(n,C) |
| gptkbp:field |
gptkb:Lie_theory
gptkb:algebra gptkb:mathematics |
| gptkbp:hasProperty |
Killing form is non-degenerate
completely reducible representations |
| https://www.w3.org/2000/01/rdf-schema#label |
Semisimple Lie algebra
|
| gptkbp:namedFor |
gptkb:Élie_Cartan
|
| gptkbp:relatedTo |
gptkb:Lie_group
solvable Lie algebra reductive Lie algebra |
| gptkbp:structure |
gptkb:root
|
| gptkbp:studiedBy |
gptkb:Élie_Cartan
19th century |
| gptkbp:used_in |
gptkb:theoretical_physics
differential geometry representation theory |
| gptkbp:bfsParent |
gptkb:Springer_resolution
|
| gptkbp:bfsLayer |
7
|