Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:Lie_group orthogonal group |
| gptkbp:actsOn |
R^{2n}
|
| gptkbp:appearsIn |
gptkb:theoretical_physics
differential geometry representation theory |
| gptkbp:centralTo |
{I, -I}
|
| gptkbp:compact |
true
|
| gptkbp:connects |
true
|
| gptkbp:definedIn |
real numbers
|
| gptkbp:determinant |
1
|
| gptkbp:dimensions |
n(2n-1)
|
| gptkbp:elements_are |
2n x 2n real orthogonal matrices with determinant 1
|
| gptkbp:fundamentalGroup |
gptkb:Z_2
|
| https://www.w3.org/2000/01/rdf-schema#label |
SO(2n)
|
| gptkbp:isSemisimple |
true
|
| gptkbp:isSimple |
true
|
| gptkbp:Lie_algebra |
so(2n)
|
| gptkbp:maximal_torus_dimension |
n
|
| gptkbp:preserves |
gptkb:Euclidean_inner_product
|
| gptkbp:quotient_by_center |
PSO(2n)
|
| gptkbp:rank |
n
|
| gptkbp:realForm |
SO(2n, C)
|
| gptkbp:relatedTo |
gptkb:Spin_group
symplectic group Sp(2n) orthogonal group O(2n) special linear group SL(2n) |
| gptkbp:type |
D_n
|
| gptkbp:universalCover |
gptkb:Spin(2n)
|
| gptkbp:bfsParent |
gptkb:n-torus_T^n
|
| gptkbp:bfsLayer |
6
|