Special Unitary Group of degree N

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:group_of_people
gptkbp:abbreviation	gptkb:SU(N)
gptkbp:appearsIn	gptkb:quantum_chromodynamics gptkb:Standard_Model_of_particle_physics gptkb:Yang-Mills_theory
gptkbp:category	group theory mathematical physics representation theory
gptkbp:centralTo	cyclic group of order N
gptkbp:compact	compact
gptkbp:compact_real_form	yes
gptkbp:definedIn	group of N x N unitary matrices with determinant 1
gptkbp:dimensions	N^2 - 1
gptkbp:field	complex numbers
gptkbp:first_Chern_class	trivial
gptkbp:fundamentalGroup	trivial for N ≥ 2
gptkbp:generator_count	N^2 - 1
gptkbp:hasSpecialCase	gptkb:SU(3) gptkb:SU(2) gptkb:SU(1)
gptkbp:heldBy	gptkb:group_of_people gptkb:Lie_group simple group compact group connected group
gptkbp:homotopy_group	π1(SU(N)) = 0 for N ≥ 2
https://www.w3.org/2000/01/rdf-schema#label	Special Unitary Group of degree N
gptkbp:irreducible_representations	classified by Young tableaux
gptkbp:isNonAbelian	yes
gptkbp:Lie_algebra	su(N)
gptkbp:maximal_torus	(N-1)-dimensional
gptkbp:quotient_group	U(N)/U(1)
gptkbp:relatedTo	gptkb:general_linear_group gptkb:projective_special_unitary_group gptkb:projective_unitary_group gptkb:unitary_group_U(N) orthogonal group projective special unitary group PSU(N) special linear group SL(N, C)
gptkbp:simply_connected	yes for N ≥ 2
gptkbp:used_in	gptkb:gauge_theory particle physics quantum mechanics representation theory theory of strong interactions
gptkbp:bfsParent	gptkb:SU(N)
gptkbp:bfsLayer	6