Statements (33)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:actsOn |
spinors
|
| gptkbp:centralTo |
Z_2 (for n odd)
Z_4 or Z_2 × Z_2 (for n even) |
| gptkbp:compact |
true
|
| gptkbp:connectedTo |
true
|
| gptkbp:fundamentalGroup |
trivial
|
| gptkbp:hasConnection |
true
|
| gptkbp:hasSubgroup |
Clifford algebra Cl(n)
|
| https://www.w3.org/2000/01/rdf-schema#label |
Spin(n)
|
| gptkbp:is_a_covering_group_of |
gptkb:SO(n)
|
| gptkbp:is_a_real_Lie_group |
true
|
| gptkbp:is_a_simple_group |
true (for n ≥ 3, except n=4)
|
| gptkbp:is_a_topological_group |
true
|
| gptkbp:is_the_double_cover_of |
gptkb:SO(n)
|
| gptkbp:isMatrixGroup |
false
|
| gptkbp:isNonAbelian |
true
|
| gptkbp:Lie_algebra |
so(n)
|
| gptkbp:relatedTo |
gptkb:Lie_group
orthogonal group Pin(n) |
| gptkbp:universalCover |
gptkb:SO(n)
|
| gptkbp:used_in |
gptkb:quantum_field_theory
gptkb:theoretical_physics gptkb:string_theory gptkb:theory_of_spinors differential geometry representation theory spin geometry |
| gptkbp:bfsParent |
gptkb:SO(n)
gptkb:SO(n,_R) gptkb:special_orthogonal_group_SO(n) |
| gptkbp:bfsLayer |
6
|