special orthogonal group SO(n, C)
GPTKB entity
Statements (28)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebraic_geometry
gptkb:group_of_people gptkb:Lie_group |
| gptkbp:actsOn |
complex n-dimensional vector space
|
| gptkbp:centralTo |
{I, -I} for even n
{I} for odd n |
| gptkbp:compact |
true
|
| gptkbp:connects |
true
|
| gptkbp:consistsOf |
n x n complex matrices
|
| gptkbp:definedIn |
complex numbers
|
| gptkbp:definesProperty |
A^T A = I
determinant = 1 |
| gptkbp:dimensions |
n(n-1)/2
|
| gptkbp:hasSubgroup |
gptkb:orthogonal_group_O(n,_C)
gptkb:general_linear_group_GL(n,_C) |
| https://www.w3.org/2000/01/rdf-schema#label |
special orthogonal group SO(n, C)
|
| gptkbp:isAlgebraicGroup |
true
|
| gptkbp:isClassicalGroup |
true
|
| gptkbp:isMatrixGroup |
true
|
| gptkbp:isNonAbelian |
true
|
| gptkbp:isReductive |
true
|
| gptkbp:isSemisimple |
true
|
| gptkbp:isSimple |
n >= 3
|
| gptkbp:Lie_algebra |
so(n, C)
|
| gptkbp:notation |
gptkb:SO(n,_C)
|
| gptkbp:relatedTo |
spin group Spin(n, C)
|
| gptkbp:bfsParent |
gptkb:orthogonal_group_SO(n)
|
| gptkbp:bfsLayer |
7
|