|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:adjointRepresentation
|
dimension N^2 - 1
|
|
gptkbp:centerOrder
|
N
|
|
gptkbp:centralTo
|
cyclic group of order N
|
|
gptkbp:compact
|
true
|
|
gptkbp:connects
|
true
|
|
gptkbp:containsElement
|
N x N unitary matrices with determinant 1
|
|
gptkbp:definedIn
|
complex numbers
|
|
gptkbp:dimensions
|
N^2 - 1
|
|
gptkbp:example
|
gptkb:SU(5)
gptkb:SU(3)
gptkb:SU(2)
|
|
gptkbp:firstChernClass
|
0
|
|
gptkbp:fullName
|
gptkb:Special_Unitary_Group_of_degree_N
|
|
gptkbp:fundamentalGroup
|
trivial
|
|
gptkbp:fundamentalRepresentation
|
N-dimensional
|
|
gptkbp:generatorCount
|
N^2 - 1
|
|
gptkbp:hasConnection
|
true
|
|
gptkbp:hasSubgroup
|
gptkb:U(N)
|
|
gptkbp:homotopyGroup
|
π_1(SU(N)) = 0
π_2(SU(N)) = 0
π_3(SU(N)) = Z
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SU(N)
|
|
gptkbp:isNonAbelian
|
N > 1
|
|
gptkbp:isSimple
|
N > 1
|
|
gptkbp:Lie_algebra
|
su(N)
|
|
gptkbp:maximalTorus
|
U(1)^{N-1}
|
|
gptkbp:notation
|
gptkb:SU(N)
|
|
gptkbp:realForm
|
gptkb:SL(N,C)
|
|
gptkbp:relatedTo
|
orthogonal group
|
|
gptkbp:simplyConnected
|
true
|
|
gptkbp:trivialFor
|
N = 1
|
|
gptkbp:type
|
A_{N-1}
|
|
gptkbp:usedAs
|
gauge group in QCD (for N=3)
gauge group in electroweak theory (for N=2)
|
|
gptkbp:usedIn
|
gptkb:gauge_theory
particle physics
quantum mechanics
representation theory
standard model
|
|
gptkbp:Weyl_group
|
gptkb:symmetric_group_S_N
|
|
gptkbp:bfsParent
|
gptkb:gauge_theory
|
|
gptkbp:bfsLayer
|
5
|