|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:topology
gptkb:Lie_group
orthogonal group
compact group
|
|
gptkbp:Cartan_matrix
|
[2]
|
|
gptkbp:centralTo
|
gptkb:Z_2
|
|
gptkbp:compact
|
true
|
|
gptkbp:compact_real_form_of
|
gptkb:SL(2,C)
|
|
gptkbp:complexification
|
gptkb:SL(2,C)
|
|
gptkbp:connects
|
true
|
|
gptkbp:containsElement
|
2x2 unitary matrices with determinant 1
|
|
gptkbp:dimensions
|
3
|
|
gptkbp:discoveredBy
|
gptkb:Élie_Cartan
|
|
gptkbp:double_cover_of
|
gptkb:SO(3)
|
|
gptkbp:first_Chern_class
|
0
|
|
gptkbp:first_homology_group
|
0
|
|
gptkbp:fundamentalGroup
|
trivial
|
|
gptkbp:generation
|
Pauli matrices
|
|
gptkbp:homotopy_type
|
gptkb:3-sphere
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SU(2) group
|
|
gptkbp:irreducible_representations
|
labeled by non-negative half-integers
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isomorphicTo
|
unit quaternions
spin group Spin(3)
|
|
gptkbp:Lie_algebra
|
gptkb:su(2)
|
|
gptkbp:maximal_torus
|
gptkb:U(1)
|
|
gptkbp:order
|
infinite
|
|
gptkbp:order_of_center
|
2
|
|
gptkbp:rank
|
1
|
|
gptkbp:realForm
|
gptkb:SU(2)
|
|
gptkbp:relatedTo
|
gptkb:rotation_group
gptkb:Hopf_fibration
quaternions
angular momentum
spin
isospin
|
|
gptkbp:simply_connected
|
true
|
|
gptkbp:type
|
A1
|
|
gptkbp:universal_cover_of
|
gptkb:SO(3)
|
|
gptkbp:used_in
|
gptkb:gauge_theory
gptkb:Yang-Mills_theory
gptkb:Standard_Model
particle physics
quantum mechanics
representation theory
|
|
gptkbp:Weyl_group
|
gptkb:Z_2
|
|
gptkbp:bfsParent
|
gptkb:SU(2)_symmetry
gptkb:SU(2)_gauge_symmetry
|
|
gptkbp:bfsLayer
|
6
|