Lorentz algebra

URI: https://gptkb.org/entity/Lorentz_algebra
GPTKB entity
Statements (31)
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
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
gptkb:Poincaré_algebra
gptkbp:bfsLayer 7
https://www.w3.org/2000/01/rdf-schema#label Lorentz algebra