Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:associatedWith |
orthogonal group
|
| gptkbp:basis_elements |
skew-symmetric matrices
|
| gptkbp:Cartan_classification |
type B and D
|
| gptkbp:centralTo |
trivial for n > 2
|
| gptkbp:dimensions |
n(n-1)/2
|
| gptkbp:field |
complex numbers
real numbers |
| gptkbp:heldBy |
simple Lie algebra (for n > 2)
|
| https://www.w3.org/2000/01/rdf-schema#label |
orthogonal Lie algebras
|
| gptkbp:is_a_subalgebra_of |
gptkb:general_linear_Lie_algebra
|
| gptkbp:Lie_bracket |
matrix commutator
|
| gptkbp:notation |
so(n)
|
| gptkbp:preserves |
non-degenerate symmetric bilinear form
|
| gptkbp:relatedTo |
rotation algebra
|
| gptkbp:structure_constants |
antisymmetric
|
| gptkbp:type_B |
so(2n+1)
|
| gptkbp:type_D |
so(2n)
|
| gptkbp:used_in |
gptkb:theoretical_physics
differential geometry representation theory |
| gptkbp:bfsParent |
gptkb:Lie_type_D_n
gptkb:B_n_series |
| gptkbp:bfsLayer |
8
|