Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:actsOn |
quaternionic vector spaces
|
| gptkbp:centralTo |
{±1}
|
| gptkbp:compact |
true
|
| gptkbp:complexification |
gptkb:SL(2,ℂ)
|
| gptkbp:connects |
true
|
| gptkbp:dimensions |
3
|
| gptkbp:fundamentalGroup |
trivial
|
| gptkbp:hasSubgroup |
Sp(n) for n ≥ 1
|
| https://www.w3.org/2000/01/rdf-schema#label |
Sp(1)
|
| gptkbp:isomorphicTo |
gptkb:SU(2)
|
| gptkbp:Lie_algebra |
sp(1)
|
| gptkbp:maximalTorus |
gptkb:U(1)
|
| gptkbp:rank |
1
|
| gptkbp:realForm |
sp(1,ℝ)
|
| gptkbp:realization |
group of unit quaternions
|
| gptkbp:relatedTo |
gptkb:SU(2)
gptkb:SO(3) gptkb:Spin(3) quaternions |
| gptkbp:simplyConnected |
true
|
| gptkbp:usedIn |
representation theory
theory of Lie groups quaternionic geometry |
| gptkbp:bfsParent |
gptkb:Sp(n)·Sp(1)
gptkb:quaternionic_projective_plane |
| gptkbp:bfsLayer |
7
|