Statements (31)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:alsoKnownAs |
gptkb:sl(2,C)
|
| gptkbp:application |
gptkb:theoretical_physics
partial differential equations quantum mechanics representation theory |
| gptkbp:automorphismGroup |
gptkb:PGL(2,C)
|
| gptkbp:CartanSubalgebraDimension |
1
|
| gptkbp:centralTo |
trivial
|
| gptkbp:commutationRelation |
[e,f]=h
[h,e]=2e [h,f]=-2f |
| gptkbp:dimensions |
3
|
| gptkbp:Dynkin_diagram |
single node
|
| gptkbp:envelopingAlgebra |
universal enveloping algebra of sl(2,C)
|
| gptkbp:field |
complex numbers
|
| gptkbp:generation |
e, f, h
|
| gptkbp:highestWeightModule |
finite-dimensional irreducible representations labeled by non-negative integers
|
| https://www.w3.org/2000/01/rdf-schema#label |
A 1 Lie algebra
|
| gptkbp:isomorphicTo |
so(3,C)
sp(2,C) |
| gptkbp:KillingForm |
non-degenerate
|
| gptkbp:rank |
1
|
| gptkbp:realForm |
gptkb:su(2)
gptkb:sl(2,R) |
| gptkbp:type |
gptkb:A_1
gptkb:Lie_group gptkb:classical_Lie_algebra |
| gptkbp:Weyl_group |
gptkb:Z/2Z
|
| gptkbp:bfsParent |
gptkb:A_{n-1}_Lie_algebra
|
| gptkbp:bfsLayer |
8
|