Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:adjointGroup |
gptkb:PSL(2,_R)
|
| gptkbp:automorphismGroup |
gptkb:PGL(2,_R)
|
| gptkbp:basisFor |
{E, F, H}
|
| gptkbp:CartanSubalgebraDimension |
1
|
| gptkbp:centralTo |
{0}
|
| gptkbp:dimensions |
3
|
| gptkbp:envelopingAlgebra |
U(sl(2, R))
|
| gptkbp:field |
real numbers
|
| gptkbp:fullName |
special linear Lie algebra of 2x2 real matrices
|
| gptkbp:hasCasimirElement |
true
|
| https://www.w3.org/2000/01/rdf-schema#label |
Lie algebra sl(2, R)
|
| gptkbp:isomorphicTo |
so(2,1)
|
| gptkbp:isSimple |
true
|
| gptkbp:KillingFormSignature |
(2,1)
|
| gptkbp:rank |
1
|
| gptkbp:realForm |
gptkb:sl(2,_C)
|
| gptkbp:relatedGroup |
gptkb:SL(2,_R)
|
| gptkbp:splitRealForm |
true
|
| gptkbp:structureConstants |
[H,E]=2E, [H,F]=-2F, [E,F]=H
|
| gptkbp:type |
A1
|
| gptkbp:usedIn |
gptkb:geometry
gptkb:theoretical_physics partial differential equations representation theory |
| gptkbp:bfsParent |
gptkb:Special_Linear_Group_of_2x2_Real_Matrices
|
| gptkbp:bfsLayer |
8
|