special orthogonal group SO(4)

URI: https://gptkb.org/entity/special_orthogonal_group_SO(4)
GPTKB entity
Statements (38)
Predicate Object
gptkbp:instanceOf gptkb:group_of_people
gptkb:Lie_group
gptkbp:actsOn gptkb:4-dimensional_Euclidean_space
gptkbp:application gptkb:geometry
gptkb:theoretical_physics
rotations in 4D space
gptkbp:Cartan_subgroup Torus T^2
gptkbp:centralTo {I, -I}
gptkbp:defines group of 4x4 real orthogonal matrices with determinant 1
gptkbp:dimensions 6
gptkbp:double_cover Spin(4)
gptkbp:field real numbers
gptkbp:fundamentalGroup gptkb:Z/2Z
gptkbp:group_order infinite
gptkbp:homotopy_group_π0 trivial
gptkbp:homotopy_group_π1 gptkb:Z/2Z
https://www.w3.org/2000/01/rdf-schema#label special orthogonal group SO(4)
gptkbp:isomorphicTo (SU(2) × SU(2))/Z2
gptkbp:Lie_algebra so(4)
gptkbp:Lie_algebra_dimension 6
gptkbp:maximal_compact_subgroup_of GL(4, R)
gptkbp:notation SO(4)
gptkbp:preserves Euclidean metric
gptkbp:rank 2
gptkbp:relatedTo orthogonal group O(4)
rotational symmetry in 4 dimensions
special orthogonal group SO(3)
spin group Spin(4)
gptkbp:split_as SO(3) × SO(3)
gptkbp:type compact
non-abelian
connected
semisimple
simple (not simple, but semisimple)
gptkbp:universalCover Spin(4)
gptkbp:Weyl_group (Z/2Z) × (Z/2Z)
gptkbp:bfsParent gptkb:special_orthogonal_group_SO(n)
gptkbp:bfsLayer 6