|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:application
|
gptkb:quantum_chromodynamics
gptkb:Standard_Model_of_particle_physics
representation theory
|
|
gptkbp:centralTo
|
cyclic group of order n
|
|
gptkbp:compact
|
true
|
|
gptkbp:connects
|
true
|
|
gptkbp:defines
|
Group of n x n unitary matrices with determinant 1
|
|
gptkbp:dimensions
|
n^2 - 1
|
|
gptkbp:example
|
gptkb:SU(3)
gptkb:SU(2)
|
|
gptkbp:field
|
complex numbers
|
|
gptkbp:firstChernClass
|
0
|
|
gptkbp:fullName
|
gptkb:Special_Unitary_Group_of_degree_n
|
|
gptkbp:fundamentalGroup
|
trivial
|
|
gptkbp:generatorCount
|
n^2 - 1
|
|
gptkbp:hasConnection
|
true
|
|
gptkbp:hasSubgroup
|
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
|
true
|
|
gptkbp:isSemisimple
|
true
|
|
gptkbp:isSimple
|
n >= 2
true for n >= 2
|
|
gptkbp:Lie_algebra
|
su(n)
|
|
gptkbp:maximalTorus
|
U(1)^{n-1}
|
|
gptkbp:notation
|
gptkb:SU(n)
|
|
gptkbp:rank
|
n-1
|
|
gptkbp:realDimension
|
n^2 - 1
|
|
gptkbp:relatedTo
|
orthogonal group
|
|
gptkbp:simplyConnected
|
true
|
|
gptkbp:type
|
A_{n-1}
compact simple Lie group
|
|
gptkbp:usedIn
|
gptkb:gauge_theory
gptkb:theoretical_physics
gptkb:topology
differential geometry
mathematical physics
particle physics
quantum mechanics
|
|
gptkbp:Weyl_group
|
gptkb:symmetric_group_S_n
|
|
gptkbp:bfsParent
|
gptkb:Kähler_manifold
gptkb:orthogonal_group
|
|
gptkbp:bfsLayer
|
5
|