Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:basisFor |
{E, F, H}
|
| gptkbp:Cartan_subalgebra |
1-dimensional
|
| gptkbp:centralTo |
{0}
|
| gptkbp:commutation_relation |
[E, F] = H
[H, E] = 2E [H, F] = -2F |
| gptkbp:dimensions |
3
|
| gptkbp:field |
complex numbers
|
| https://www.w3.org/2000/01/rdf-schema#label |
sl(2, ℂ)
|
| gptkbp:is_the_Lie_algebra_of |
gptkb:SL(2,_ℂ)
|
| gptkbp:isSemisimple |
true
|
| gptkbp:isSimple |
true
|
| gptkbp:Killing_form |
non-degenerate
|
| gptkbp:rank |
1
|
| gptkbp:realForm |
sl(2, ℝ)
|
| gptkbp:representation_theory |
well-studied
|
| gptkbp:type |
A1
|
| gptkbp:used_in |
gptkb:theory_of_special_relativity
quantum mechanics representation theory |
| gptkbp:bfsParent |
gptkb:Projective_linear_group_PGL(2,_ℂ)
|
| gptkbp:bfsLayer |
7
|