Statements (30)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:basisFor |
generators of rotations and boosts
|
| gptkbp:category |
gptkb:algebra
|
| gptkbp:commutation_relations |
[J_i, J_j] = i ε_{ijk} J_k
[J_i, K_j] = i ε_{ijk} K_k [K_i, K_j] = -i ε_{ijk} J_k |
| gptkbp:dimensions |
6
|
| gptkbp:field |
gptkb:mathematics
gptkb:theoretical_physics mathematical physics |
| gptkbp:has_subalgebra |
gptkb:rotation_algebra_so(3)
boost algebra |
| https://www.w3.org/2000/01/rdf-schema#label |
Lorentz algebra
|
| gptkbp:is_the_Lie_algebra_of |
gptkb:Lorentz_group
|
| gptkbp:namedAfter |
gptkb:Hendrik_Lorentz
|
| gptkbp:notation |
so(1,3)
𝔰𝔬(1,3) |
| gptkbp:rank |
complex numbers
real numbers |
| gptkbp:relatedConcept |
gptkb:Casimir_operator
representation theory spinor representation |
| gptkbp:relatedTo |
gptkb:Lorentz_group
|
| gptkbp:structure_constants |
antisymmetric
|
| gptkbp:subalgebra_of |
gptkb:Poincaré_algebra
|
| gptkbp:used_in |
gptkb:general_relativity
gptkb:quantum_field_theory gptkb:special_relativity |
| gptkbp:bfsParent |
gptkb:Lorentz_group
|
| gptkbp:bfsLayer |
6
|