special unitary group SU(n)

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:group_of_people gptkb:Lie_group
gptkbp:centralTo	cyclic group of order n
gptkbp:compact	true
gptkbp:connects	true
gptkbp:consistsOf	n x n unitary matrices with determinant 1
gptkbp:definedIn	complex numbers
gptkbp:dimensions	n^2 - 1
gptkbp:example	gptkb:SU(3) gptkb:SU(2)
gptkbp:fundamentalGroup	cyclic group of order n
gptkbp:generation	Hermitian traceless matrices
gptkbp:hasSubgroup	gptkb:unitary_group_U(n)
https://www.w3.org/2000/01/rdf-schema#label	special unitary group SU(n)
gptkbp:isNonAbelian	for n >= 2
gptkbp:isomorphicTo	3-sphere for SU(2)
gptkbp:isSimple	n >= 2
gptkbp:Lie_algebra	gptkb:special_unitary_algebra_su(n)
gptkbp:maximalTorus	diagonal matrices with determinant 1
gptkbp:notation	gptkb:SU(n)
gptkbp:rank	n-1
gptkbp:realDimension	n^2 - 1
gptkbp:realForm	gptkb:special_linear_group_SL(n,_C)
gptkbp:relatedTo	gptkb:special_linear_group_SL(n,_C) gptkb:symplectic_group_Sp(n) gptkb:unitary_group_U(n) gptkb:orthogonal_group_SO(n)
gptkbp:usedIn	gptkb:gauge_theory gptkb:quantum_chromodynamics_(QCD) gptkb:Standard_Model_of_particle_physics particle physics quantum mechanics representation theory
gptkbp:bfsParent	gptkb:Lie_group
gptkbp:bfsLayer	5