Special orthogonal group over complex numbers
GPTKB entity
Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:Lie_group |
| gptkbp:center_for_n_even |
{I}
|
| gptkbp:center_for_n_odd |
{I, -I}
|
| gptkbp:connects |
true
|
| gptkbp:definedIn |
group of n×n complex matrices preserving a non-degenerate symmetric bilinear form and with determinant 1
|
| gptkbp:dimensions |
n(n-1)/2
|
| gptkbp:field |
complex numbers
|
| gptkbp:hasSubgroup |
Orthogonal group over complex numbers
Special linear group over complex numbers |
| https://www.w3.org/2000/01/rdf-schema#label |
Special orthogonal group over complex numbers
|
| gptkbp:Lie_algebra |
so(n, C)
|
| gptkbp:notation |
gptkb:SO(n,_C)
|
| gptkbp:rank |
floor(n/2)
|
| gptkbp:relatedTo |
Orthogonal group over complex numbers
Special orthogonal group over real numbers Spin group over complex numbers |
| gptkbp:simple_for_n_≥_3 |
true
|
| gptkbp:type |
complex simple Lie group (for n ≥ 3)
|
| gptkbp:used_in |
gptkb:algebraic_geometry
gptkb:theoretical_physics representation theory |
| gptkbp:bfsParent |
gptkb:Special_orthogonal_group_of_signature_(1,n)
|
| gptkbp:bfsLayer |
7
|