special unitary group SU(2)

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:group_of_people gptkb:topology gptkb:Lie_group compact group
gptkbp:Cartan_matrix	[2]
gptkbp:centralTo	{±I}
gptkbp:compact	true
gptkbp:compact_real_form_of	gptkb:SL(2,C)
gptkbp:connects	true
gptkbp:definedIn	group of 2x2 unitary matrices with determinant 1
gptkbp:dimensions	3
gptkbp:field	complex numbers
gptkbp:fundamentalGroup	trivial
gptkbp:generation	Pauli matrices
https://www.w3.org/2000/01/rdf-schema#label	special unitary group SU(2)
gptkbp:isomorphicTo	unit quaternions 3-sphere S^3
gptkbp:Lie_algebra	gptkb:su(2)
gptkbp:maximal_torus	gptkb:U(1)
gptkbp:notation	gptkb:SU(2)
gptkbp:order	infinite
gptkbp:rank	1
gptkbp:real_dimension	3
gptkbp:relatedTo	gptkb:unitary_group_U(2) gptkb:rotation_group_SO(3) quaternions spin group Spin(3) special linear group SL(2,C)
gptkbp:represents	irreducible representations labeled by spin j=0,1/2,1,3/2,...
gptkbp:simply_connected	true
gptkbp:type	A1
gptkbp:universal_cover_of	special orthogonal group SO(3)
gptkbp:used_in	gptkb:gauge_theory particle physics quantum mechanics representation theory angular momentum spin
gptkbp:Weyl_group	gptkb:Z/2Z
gptkbp:bfsParent	gptkb:special_unitary_group_SU(3)
gptkbp:bfsLayer	7