Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
orthogonal group |
| gptkbp:centralTo |
{I, -I} (for n+1 even)
{I} (for n+1 odd) |
| gptkbp:compact |
true
|
| gptkbp:definedIn |
complex numbers
|
| gptkbp:determinant |
1
|
| gptkbp:dimensions |
(n+1)n/2
|
| gptkbp:hasConnection |
true
|
| gptkbp:hasSubgroup |
GL(n+1, ℂ)
O(n+1, ℂ) |
| https://www.w3.org/2000/01/rdf-schema#label |
SO(n+1, ℂ)
|
| gptkbp:isAlgebraicGroup |
true
|
| gptkbp:isMatrixGroup |
true
|
| gptkbp:isReductive |
true
|
| gptkbp:isSimple |
true (for n+1 ≥ 3)
|
| gptkbp:Lie_algebra |
so(n+1, ℂ)
|
| gptkbp:preserves |
complex symmetric bilinear form
|
| gptkbp:rank |
n
|
| gptkbp:relatedTo |
orthogonal group
|
| gptkbp:bfsParent |
gptkb:SO(n+1)
|
| gptkbp:bfsLayer |
7
|