Statements (17)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
gptkb:finite-dimensional_Lie_groups
|
| gptkbp:field |
gptkb:Lie_theory
gptkb:mathematics differential geometry |
| https://www.w3.org/2000/01/rdf-schema#label |
Lie's first theorem
|
| gptkbp:implies |
existence of a local Lie group homomorphism for every Lie algebra homomorphism
|
| gptkbp:namedAfter |
gptkb:Sophus_Lie
|
| gptkbp:partOf |
gptkb:Lie's_three_theorems
|
| gptkbp:publishedIn |
19th century
|
| gptkbp:relatedTo |
gptkb:Lie's_second_theorem
gptkb:Lie's_third_theorem gptkb:Lie_group |
| gptkbp:state |
Every finite-dimensional Lie algebra of a Lie group is the tangent space at the identity with the Lie bracket induced by the group commutator.
|
| gptkbp:bfsParent |
gptkb:Lie_theory
gptkb:Lie_group |
| gptkbp:bfsLayer |
5
|