Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:Lie_group |
| gptkbp:application |
gptkb:algebraic_geometry
gptkb:theoretical_physics differential geometry representation theory |
| gptkbp:centralTo |
{I, -I} (for n+1 even)
{I} (for n+1 odd) |
| gptkbp:defines |
Group of (n+1)x(n+1) complex matrices preserving a non-degenerate symmetric bilinear form and with determinant 1
|
| gptkbp:dimensions |
(n+1)n/2
|
| gptkbp:field |
complex numbers
|
| gptkbp:fullName |
Special Orthogonal Group of degree n+1 over the complex numbers
|
| gptkbp:hasSubgroup |
GL(n+1,C)
SL(n+1,C) SO(n+1,R) SO(n,C) |
| https://www.w3.org/2000/01/rdf-schema#label |
SO(n+1,C)
|
| gptkbp:Lie_algebra |
so(n+1,C)
|
| gptkbp:maximalCompactSubgroup |
gptkb:SO(n+1)
|
| gptkbp:notation |
SO(n+1,ℂ)
|
| gptkbp:relatedGroup |
gptkb:Lie_group
connected non-compact semisimple simple Lie group (for n+1 > 2) |
| gptkbp:relatedTo |
orthogonal group O(n+1,C)
special linear group SL(n+1,C) |
| gptkbp:rootSystemType |
B_k (if n+1=2k+1)
D_k (if n+1=2k) |
| gptkbp:universalCover |
Spin(n+1,C)
|
| gptkbp:bfsParent |
gptkb:SO^+(1,n)
|
| gptkbp:bfsLayer |
7
|