Statements (31)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:centralTo |
Z_4 (for n odd)
Z_2 × Z_2 (for n even, n>2) |
| gptkbp:compact |
true
|
| gptkbp:connectedTo |
true
|
| gptkbp:dimensions |
n(2n-1)
|
| gptkbp:fundamentalGroup |
trivial
|
| gptkbp:has_spinor_representations |
true
|
| gptkbp:hasConnection |
true
|
| gptkbp:hasSubgroup |
Clifford algebra Cl(2n)
|
| https://www.w3.org/2000/01/rdf-schema#label |
Spin(2n)
|
| gptkbp:is_a_classical_group |
true
|
| gptkbp:is_a_covering_group_of |
gptkb:SO(2n)
|
| gptkbp:is_a_double_cover_of |
gptkb:SO(2n)
|
| gptkbp:is_a_real_Lie_group |
true
|
| gptkbp:is_a_simple_Lie_group |
true
|
| gptkbp:is_a_universal_cover_of |
gptkb:SO(2n)
|
| gptkbp:isMatrixGroup |
false
|
| gptkbp:Lie_algebra |
so(2n)
|
| gptkbp:realForm |
Spin(2n,C)
|
| gptkbp:relatedTo |
orthogonal group
Pin(2n) |
| gptkbp:used_in |
gptkb:string_theory
gptkb:theory_of_spinors differential geometry mathematical physics representation theory |
| gptkbp:bfsParent |
gptkb:SO(2n)
gptkb:D_n_Lie_algebra gptkb:D_n_root_system |
| gptkbp:bfsLayer |
7
|