Statements (25)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
orthogonal group |
| gptkbp:actsOn |
R^{4n}
|
| gptkbp:centralTo |
{I, -I}
|
| gptkbp:compact |
true
|
| gptkbp:connectedTo |
true
|
| gptkbp:determinant |
1
|
| gptkbp:dimensions |
4n(4n-1)/2
|
| gptkbp:elements_are |
4n x 4n real orthogonal matrices with determinant 1
|
| gptkbp:fundamentalGroup |
gptkb:Z_2
|
| gptkbp:hasSubgroup |
O(4n)
SO(4n+1) |
| https://www.w3.org/2000/01/rdf-schema#label |
SO(4n)
|
| gptkbp:isSimple |
true (for n>1)
|
| gptkbp:Lie_algebra |
so(4n)
|
| gptkbp:maximal_compact_subgroup_of |
SO(4n, C)
|
| gptkbp:preserves |
Euclidean metric
|
| gptkbp:realForm |
SO(4n, C)
|
| gptkbp:relatedTo |
O(4n)
SO(4n+1) SO(4n-1) Spin(4n) |
| gptkbp:universalCover |
Spin(4n)
|
| gptkbp:bfsParent |
gptkb:Sp(n)·Sp(1)
|
| gptkbp:bfsLayer |
7
|