Lie algebra su(2)

URI: https://gptkb.org/entity/Lie_algebra_su(2)
GPTKB entity
Statements (32)
Predicate Object
gptkbp:instanceOf gptkb:Lie_group
gptkbp:basisFor Pauli matrices
gptkbp:Cartan_subalgebra_dimension 1
gptkbp:centralTo trivial
gptkbp:commutation_relations [X,Y]=Z, [Y,Z]=X, [Z,X]=Y (up to sign and normalization)
gptkbp:compact true
gptkbp:complexification gptkb:sl(2,C)
gptkbp:dimensions 3
gptkbp:field complex numbers
real numbers
gptkbp:generation Jx
Jy
Jz
gptkbp:highest_weight_representations finite-dimensional irreducible representations labeled by non-negative integers
https://www.w3.org/2000/01/rdf-schema#label Lie algebra su(2)
gptkbp:isomorphicTo so(3)
gptkbp:isSemisimple true
gptkbp:isSimple true
gptkbp:Killing_form non-degenerate
gptkbp:rank 1
gptkbp:real_dimension 3
gptkbp:realForm gptkb:Lie_algebra_sl(2,C)
gptkbp:relatedGroup gptkb:SU(2)
gptkbp:root_multiplicity 1
gptkbp:structure_constants gptkb:Levi-Civita_symbol
gptkbp:type A1
gptkbp:used_in gptkb:theoretical_physics
quantum mechanics
representation theory
gptkbp:bfsParent gptkb:Pauli_Y_matrix
gptkb:Pauli_Z_matrix
gptkbp:bfsLayer 6