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gptkbp:instanceOf
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gptkb:Lie_group
|
|
gptkbp:application
|
gptkb:Grand_Unified_Theories
gptkb:Quantum_Chromodynamics_(SU(3))
gptkb:Standard_Model_(SU(3),_SU(2))
|
|
gptkbp:associatedWith
|
orthogonal group
|
|
gptkbp:basisFor
|
generators T^a (a=1,...,N^2-1)
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|
gptkbp:CartanSubalgebraDimension
|
gptkb:N-1
|
|
gptkbp:centralTo
|
trivial for N=2, Z_N for N>2
|
|
gptkbp:commutationRelation
|
[T^a, T^b] = i f^{abc} T^c
|
|
gptkbp:compact
|
true
|
|
gptkbp:definesProperty
|
Lie bracket is commutator
traceless anti-Hermitian N x N matrices
|
|
gptkbp:dimensions
|
N^2 - 1
|
|
gptkbp:field
|
gptkb:mathematics
gptkb:theoretical_physics
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SU(N) algebra
|
|
gptkbp:isSimple
|
true
|
|
gptkbp:notation
|
su(N)
|
|
gptkbp:rank
|
gptkb:N-1
|
|
gptkbp:realForm
|
su(N)
|
|
gptkbp:relatedTo
|
gptkb:special_linear_group_SL(N)
gptkb:unitary_group_U(N)
|
|
gptkbp:represents
|
adjoint representation
fundamental representation
|
|
gptkbp:structureConstants
|
f^{abc}
|
|
gptkbp:type
|
A_{N-1}
|
|
gptkbp:usedIn
|
gptkb:gauge_theory
gptkb:quantum_field_theory
particle physics
|
|
gptkbp:bfsParent
|
gptkb:SU(3)_algebra
|
|
gptkbp:bfsLayer
|
6
|