Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:alsoKnownAs |
special orthogonal Lie algebra of degree n+1 over the complex numbers
|
| gptkbp:basisFor |
skew-symmetric (n+1)x(n+1) complex matrices
|
| gptkbp:CartanSubalgebra |
diagonal matrices with zero trace and purely imaginary entries
|
| gptkbp:centralTo |
trivial (for n+1 > 2)
|
| gptkbp:complexification |
so(n+1, R)
|
| gptkbp:definingRelation |
[X,Y] = XY - YX for X,Y skew-symmetric matrices
|
| gptkbp:dimensions |
(n+1)*n/2
|
| gptkbp:field |
complex numbers
|
| https://www.w3.org/2000/01/rdf-schema#label |
Lie algebra so(n+1, C)
|
| gptkbp:KillingForm |
non-degenerate
|
| gptkbp:rank |
n
|
| gptkbp:realForm |
so(n+1, R)
|
| gptkbp:relatedGroup |
gptkb:SO(n+1,_C)
|
| gptkbp:structureConstants |
antisymmetric
|
| gptkbp:subclassOf |
gl(n+1, C)
|
| gptkbp:type |
simple Lie algebra (for n+1 > 3)
type B_n (if n odd), type D_n (if n even) |
| gptkbp:usedIn |
gptkb:theoretical_physics
differential geometry representation theory |
| gptkbp:bfsParent |
gptkb:SO(n+1,_C)
|
| gptkbp:bfsLayer |
7
|