Special orthogonal group of degree n+1 over the complex numbers
GPTKB entity
Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:Lie_group |
| gptkbp:alsoKnownAs |
gptkb:SO(n+1,_C)
|
| gptkbp:application |
gptkb:algebraic_geometry
gptkb:theoretical_physics representation theory |
| gptkbp:centralTo |
{I, -I} (for n+1 even)
{I} (for n+1 odd) |
| gptkbp:definedIn |
determinant 1
preserves a non-degenerate symmetric bilinear form |
| gptkbp:dimensions |
(n+1)n/2
|
| gptkbp:field |
complex numbers
|
| gptkbp:hasSubgroup |
General linear group of degree n+1 over the complex numbers
|
| https://www.w3.org/2000/01/rdf-schema#label |
Special orthogonal group of degree n+1 over the complex numbers
|
| gptkbp:Lie_algebra |
so(n+1, C)
|
| gptkbp:relatedGroup |
gptkb:algebraic_geometry
connected non-compact simple Lie group (for n+1 > 2) |
| gptkbp:relatedTo |
orthogonal group of degree n+1 over the complex numbers
special orthogonal group of degree n+1 over the real numbers |
| gptkbp:bfsParent |
gptkb:SO(n+1,_C)
|
| gptkbp:bfsLayer |
7
|