Statements (30)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:application |
representation theory
rigid body dynamics 3D rotations |
| gptkbp:associatedWith |
special orthogonal group SO(3)
|
| gptkbp:basisFor |
skew-symmetric 3x3 matrices
|
| gptkbp:CartanSubalgebraDimension |
1
|
| gptkbp:centralTo |
trivial
|
| gptkbp:commutationRelations |
[J_i, J_j] = ε_{ijk} J_k
|
| gptkbp:compact |
yes
|
| gptkbp:dimensions |
3
|
| gptkbp:field |
real numbers
|
| gptkbp:generation |
J_x, J_y, J_z
|
| https://www.w3.org/2000/01/rdf-schema#label |
rotation algebra so(3)
|
| gptkbp:isomorphicTo |
gptkb:Lie_algebra_su(2)
|
| gptkbp:isSimple |
yes
|
| gptkbp:KillingForm |
non-degenerate
|
| gptkbp:rank |
1
|
| gptkbp:realForm |
compact real form
|
| gptkbp:realization |
angular momentum operators in quantum mechanics
|
| gptkbp:relatedTo |
gptkb:rotation_group_SO(3)
|
| gptkbp:structureConstants |
gptkb:Levi-Civita_symbol
|
| gptkbp:type |
A1
|
| gptkbp:usedIn |
gptkb:mathematics
computer vision mechanics physics robotics |
| gptkbp:bfsParent |
gptkb:Lorentz_algebra
|
| gptkbp:bfsLayer |
7
|