Statements (29)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:alsoKnownAs |
so(2n+1)
|
| gptkbp:automorphismGroup |
SO(2n+1)
|
| gptkbp:Cartan_subalgebra_dimension |
n
|
| gptkbp:centralTo |
trivial
|
| gptkbp:class |
gptkb:classical_Lie_algebra
|
| gptkbp:dimensions |
n(2n+1)
|
| gptkbp:Dynkin_type |
B_n
|
| gptkbp:field_of_definition |
any field of characteristic ≠ 2
|
| gptkbp:first_simple_case |
so(3)
|
| https://www.w3.org/2000/01/rdf-schema#label |
simple Lie algebra B n
|
| gptkbp:Killing_form |
non-degenerate
|
| gptkbp:rank |
complex numbers
n |
| gptkbp:realForm |
so(p,q) with p+q=2n+1
|
| gptkbp:relatedGroup |
SO(2n+1)
Spin(2n+1) |
| gptkbp:relatedTo |
gptkb:Lie_group
orthogonal group spin representation Lie group B_n |
| gptkbp:structure_constants |
antisymmetric
|
| gptkbp:type |
B_n root system
|
| gptkbp:usedIn |
gptkb:theoretical_physics
differential geometry representation theory |
| gptkbp:Weyl_group |
hyperoctahedral group
|
| gptkbp:bfsParent |
gptkb:B_n^{(1)}
|
| gptkbp:bfsLayer |
7
|