special unitary group SU(3)

URI: https://gptkb.org/entity/special_unitary_group_SU(3)
GPTKB entity
Statements (45)
Predicate Object
gptkbp:instanceOf gptkb:group_of_people
gptkb:Lie_group
gptkbp:adjoint_representation 8-dimensional
gptkbp:appliesTo gptkb:gauge_theory
standard model of particle physics
gptkbp:Cartan_subalgebra 2-dimensional
gptkbp:centralTo cyclic group of order 3
gptkbp:compact true
gptkbp:compact_real_form gptkb:SU(3)
gptkbp:connects true
gptkbp:containsElement 3×3 unitary matrices with determinant 1
gptkbp:dimensions 8
gptkbp:discoveredBy mathematicians in early 20th century
gptkbp:first_Chern_class zero
gptkbp:fundamental_representation 3-dimensional
gptkbp:generation gptkb:Gell-Mann_matrices
gptkbp:homotopy_group_π1 gptkb:Z/3Z
gptkbp:homotopy_group_π2 0
gptkbp:homotopy_group_π3 Z
https://www.w3.org/2000/01/rdf-schema#label special unitary group SU(3)
gptkbp:Lie_algebra gptkb:su(3)
gptkbp:maximal_compact_subgroup_of gptkb:SL(3,C)
gptkbp:maximal_torus gptkb:U(1)_×_U(1)
gptkbp:non-compact_real_form gptkb:SU(2,1)
gptkbp:notation gptkb:SU(3)
gptkbp:order infinite
gptkbp:rank 2
gptkbp:realForm SU(3), SL(3,R), SU(2,1)
gptkbp:relatedConcept gptkb:color_SU(3)
gptkb:flavor_SU(3)
gptkbp:relatedTo gptkb:special_unitary_group_SU(n)
gptkb:projective_special_unitary_group_PSU(3)
gptkb:special_linear_group_SL(3,C)
gptkb:special_unitary_group_SU(2)
gptkb:unitary_group_U(3)
gptkbp:root_lattice hexagonal lattice
gptkbp:simply_connected true
gptkbp:type gptkb:A2
gptkbp:used_in gptkb:quantum_chromodynamics
particle physics
theory of strong interactions
eightfold way
gptkbp:Weyl_group gptkb:symmetric_group_S3
gptkbp:bfsParent gptkb:Lie_algebra_su(3)
gptkbp:bfsLayer 6