Statements (28)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:associatedWith |
gptkb:SU(2)_group
|
| gptkbp:basisFor |
Pauli matrices
|
| gptkbp:CartanSubalgebraDimension |
1
|
| gptkbp:CasimirOperator |
T^2 = T1^2 + T2^2 + T3^2
|
| gptkbp:centralTo |
trivial
|
| gptkbp:commutationRelations |
[T_i, T_j] = i ε_{ijk} T_k
|
| gptkbp:compact |
true
|
| gptkbp:complexification |
gptkb:sl(2,C)
|
| gptkbp:dimensions |
3
|
| gptkbp:generation |
T1, T2, T3
|
| gptkbp:highestWeightRepresentations |
labeled by half-integers
|
| https://www.w3.org/2000/01/rdf-schema#label |
SU(2) algebra
|
| gptkbp:isomorphicTo |
so(3) algebra over complex numbers
|
| gptkbp:isSimple |
true
|
| gptkbp:rank |
1
|
| gptkbp:realForm |
compact
|
| gptkbp:realization |
2x2 traceless Hermitian matrices
|
| gptkbp:relatedTo |
angular momentum
spin |
| gptkbp:structureConstants |
gptkb:Levi-Civita_symbol
|
| gptkbp:type |
A1
|
| gptkbp:universalEnvelopingAlgebra |
gptkb:U(su(2))
|
| gptkbp:usedIn |
particle physics
quantum mechanics representation theory |
| gptkbp:bfsParent |
gptkb:SU(3)_algebra
|
| gptkbp:bfsLayer |
6
|