Special orthogonal group in n+1 dimensions
GPTKB entity
Statements (30)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:alsoKnownAs |
gptkb:SO(n+1)
|
| gptkbp:application |
gptkb:geometry
computer graphics physics robotics |
| gptkbp:centralTo |
{I, -I} for even n+1
{I} for odd n+1 |
| gptkbp:compact |
true
|
| gptkbp:consistsOf |
(n+1)x(n+1) orthogonal matrices with determinant 1
|
| gptkbp:definedIn |
real numbers
|
| gptkbp:dimensions |
(n+1)n/2
|
| gptkbp:fundamentalGroup |
Z_2 for n+1 > 2
trivial for n+1 = 2 |
| gptkbp:hasConnection |
true
|
| gptkbp:hasSubgroup |
orthogonal group in n+1 dimensions
|
| https://www.w3.org/2000/01/rdf-schema#label |
Special orthogonal group in n+1 dimensions
|
| gptkbp:identityElement |
identity matrix
|
| gptkbp:isSimple |
true (for n+1 > 2)
|
| gptkbp:Lie_algebra |
so(n+1)
|
| gptkbp:realForm |
special orthogonal group over complex numbers
|
| gptkbp:relatedGroup |
gptkb:group_of_people
gptkb:rotation_group orthogonal group special group |
| gptkbp:relatedTo |
gptkb:Euclidean_space
orthogonal transformations rotation symmetry |
| gptkbp:bfsParent |
gptkb:SO(n+1)
|
| gptkbp:bfsLayer |
7
|