Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
finite-dimensional representations
algebraically closed fields of characteristic 0 solvable Lie algebras |
| gptkbp:field |
gptkb:mathematics
gptkb:Lie_algebras representation theory |
| https://www.w3.org/2000/01/rdf-schema#label |
Lie's theorem
|
| gptkbp:implies |
representation is upper triangularizable
|
| gptkbp:namedAfter |
gptkb:Sophus_Lie
|
| gptkbp:provenBy |
gptkb:Sophus_Lie
|
| gptkbp:publishedIn |
theory of Lie algebras
|
| gptkbp:relatedTo |
gptkb:Lie_group
gptkb:Engel's_theorem solvable algebra |
| gptkbp:sentence |
Every finite-dimensional representation of a solvable Lie algebra over an algebraically closed field of characteristic 0 has a common eigenvector.
|
| gptkbp:bfsParent |
gptkb:Lie_algebras
gptkb:Levi_decomposition |
| gptkbp:bfsLayer |
6
|