Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:centralTo |
Z_2 (for n+1 ≥ 3)
|
| gptkbp:hasConnection |
true
|
| gptkbp:hasSubgroup |
Clifford algebra Cl(n+1)
|
| https://www.w3.org/2000/01/rdf-schema#label |
Spin(n+1)
|
| gptkbp:importantFor |
gptkb:topology
representation theory |
| gptkbp:is_a_compact_group |
true
|
| gptkbp:is_a_connected_Lie_group |
true
|
| gptkbp:is_a_covering_group_of |
gptkb:SO(n+1)
|
| gptkbp:is_a_double_cover_of |
gptkb:SO(n+1)
|
| gptkbp:is_a_matrix_group_for_small_n |
true
|
| gptkbp:is_a_real_Lie_group |
true
|
| gptkbp:is_a_simple_Lie_group_for_n+1_≥_3 |
true
|
| gptkbp:realForm |
complex spin group Spin(n+1, C)
|
| gptkbp:relatedTo |
orthogonal group
spin structure spin representation |
| gptkbp:universalCover |
gptkb:SO(n+1)
|
| gptkbp:used_in |
gptkb:theoretical_physics
gptkb:theory_of_spinors differential geometry |
| gptkbp:bfsParent |
gptkb:SO(n+1)
|
| gptkbp:bfsLayer |
7
|