Statements (25)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:basisFor |
{E, F, H}
|
| gptkbp:centralTo |
0
|
| gptkbp:commutation_relation |
[E, F] = H
[H, E] = 2E [H, F] = -2F |
| gptkbp:dimensions |
3
|
| gptkbp:field |
real numbers
|
| https://www.w3.org/2000/01/rdf-schema#label |
sl(2, R)
|
| gptkbp:isSimple |
true
|
| gptkbp:Killing_form |
non-degenerate
|
| gptkbp:matrixRepresentation |
2x2 real traceless matrices
|
| gptkbp:rank |
1
|
| gptkbp:realForm |
gptkb:sl(2,_C)
|
| gptkbp:relatedGroup |
gptkb:SL(2,_R)
|
| gptkbp:split_real_form |
gptkb:sl(2,_C)
|
| gptkbp:used_in |
gptkb:quantum_field_theory
gptkb:theoretical_physics gptkb:hyperbolic_geometry differential geometry representation theory |
| gptkbp:bfsParent |
gptkb:SL(2,_R)
gptkb:Special_Linear_Group_of_2x2_real_matrices gptkb:PSL(2,_R) |
| gptkbp:bfsLayer |
7
|