Statements (31)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:centralTo |
{I, -I} (for n even)
{I} (for n odd) |
| gptkbp:connects |
true
|
| gptkbp:containsElement |
n x n complex matrices
|
| gptkbp:definedIn |
complex numbers
|
| gptkbp:dimensions |
n(n-1)/2
|
| gptkbp:fullName |
Special orthogonal group over the complex numbers
|
| gptkbp:hasSubgroup |
O(n, C)
|
| https://www.w3.org/2000/01/rdf-schema#label |
SO(n, C)
|
| gptkbp:isSimple |
n >= 3
|
| gptkbp:Lie_algebra |
so(n, C)
|
| gptkbp:notation |
gptkb:SO(n,_C)
|
| gptkbp:property |
orthogonal matrices
determinant 1 preserves complex bilinear form |
| gptkbp:realForm |
gptkb:SO(n)
|
| gptkbp:relatedGroup |
gptkb:algebraic_geometry
gptkb:group_of_people gptkb:Lie_group |
| gptkbp:relatedTo |
gptkb:SL(n,_C)
gptkb:SU(n) O(n, C) Spin(n, C) |
| gptkbp:usedIn |
gptkb:algebraic_geometry
gptkb:theoretical_physics differential geometry number theory representation theory |
| gptkbp:bfsParent |
gptkb:SO(n)
|
| gptkbp:bfsLayer |
6
|