|
gptkbp:instanceOf
|
gptkb:mathematical_concept
|
|
gptkbp:application
|
particle physics
quantum mechanics
representation theory
|
|
gptkbp:compact
|
true
|
|
gptkbp:connects
|
true
|
|
gptkbp:containsElement
|
gptkb:unitary_matrix
|
|
gptkbp:defines
|
group of unitary matrices under matrix multiplication
|
|
gptkbp:dimensions
|
n^2
|
|
gptkbp:example
|
gptkb:U(1)
gptkb:U(2)
gptkb:U(3)
|
|
gptkbp:field
|
gptkb:mathematics
group theory
|
|
gptkbp:hasSpecialCase
|
gptkb:orthogonal_group
|
|
gptkbp:notation
|
U(n)
|
|
gptkbp:property
|
non-abelian for n > 1
closed under matrix multiplication
closed under taking inverses
contains identity matrix
|
|
gptkbp:rank
|
complex numbers
|
|
gptkbp:relatedTo
|
gptkb:general_linear_group
gptkb:group_of_people
gptkb:Lie_group
gptkb:orthogonal_group
|
|
gptkbp:usedIn
|
gptkb:gauge_theory
gptkb:quantum_computing
standard model of particle physics
|
|
gptkbp:bfsParent
|
gptkb:Bott_periodicity_theorem
gptkb:Howe_correspondence
gptkb:theta_correspondence
gptkb:Raoul_Bott_periodicity_theorem
|
|
gptkbp:bfsLayer
|
7
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
unitary groups
|