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gptkbp:instanceOf
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gptkb:group_of_people
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|
gptkbp:application
|
gptkb:gauge_theory
differential geometry
particle physics
quantum mechanics
random matrix theory
|
|
gptkbp:centerOrder
|
infinite
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|
gptkbp:centralTo
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gptkb:U(1)
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|
gptkbp:compact
|
true
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gptkbp:connects
|
true
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gptkbp:defines
|
the group of N×N unitary matrices
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|
gptkbp:determinant
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complex number of modulus 1
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gptkbp:dimensions
|
N^2
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|
gptkbp:field
|
gptkb:mathematics
gptkb:quantum_physics
group theory
representation theory
|
|
gptkbp:firstChernClass
|
generator of H^2(BU(N), Z)
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|
gptkbp:fullName
|
unitary group of degree N
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|
gptkbp:fundamentalGroup
|
Z
|
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gptkbp:generation
|
N^2 Hermitian matrices
|
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gptkbp:hasSpecialCase
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gptkb:U(1)
gptkb:U(2)
gptkb:U(3)
|
|
gptkbp:hasSubgroup
|
gptkb:SU(N)
GL(N, C)
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|
gptkbp:homomorphism
|
det: U(N) → U(1)
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|
gptkbp:homotopyGroup
|
π_1(U(N)) = Z
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
U(N)
|
|
gptkbp:isQuotientOf
|
U(N)/SU(N) ≅ U(1)
|
|
gptkbp:Lie_algebra
|
u(N)
|
|
gptkbp:matrixCondition
|
U†U = I
|
|
gptkbp:matrixRepresentation
|
complex matrix
|
|
gptkbp:matrixSize
|
N×N
|
|
gptkbp:maximalTorus
|
U(1)^N
|
|
gptkbp:notation
|
gptkb:U(N)
|
|
gptkbp:parameter
|
N^2 real parameters
|
|
gptkbp:realDimension
|
N^2
|
|
gptkbp:relatedConcept
|
special unitary group SU(N)
general linear group GL(N, C)
orthogonal group O(N)
|
|
gptkbp:relatedGroup
|
gptkb:Lie_group
|
|
gptkbp:topology
|
compact
connected
|
|
gptkbp:usedIn
|
gptkb:gauge_theory
gptkb:quantum_field_theory
gptkb:quantum_information_theory
standard model of particle physics
fiber bundles
|
|
gptkbp:bfsParent
|
gptkb:gauge_theory
|
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gptkbp:bfsLayer
|
5
|