Statements (28)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:Lie_group |
| gptkbp:centralTo |
{I, -I} (for n+1 even)
{I} (for n+1 odd) |
| gptkbp:compact |
true
|
| gptkbp:defines |
Group of (n+1)x(n+1) complex matrices preserving a non-degenerate symmetric bilinear form and with determinant 1
|
| gptkbp:dimensions |
(n+1)n/2
|
| gptkbp:field |
complex numbers
|
| gptkbp:fullName |
gptkb:Special_orthogonal_group_of_degree_n+1_over_the_complex_numbers
|
| gptkbp:hasConnection |
true
|
| gptkbp:hasMaximalSubgroup |
gptkb:SO(n+1)
|
| gptkbp:hasSubgroup |
gptkb:GL(n+1,_C)
O(n+1, C) |
| https://www.w3.org/2000/01/rdf-schema#label |
SO(n+1, C)
|
| gptkbp:isSemisimple |
true
|
| gptkbp:isSimple |
true
|
| gptkbp:Lie_algebra |
so(n+1, C)
|
| gptkbp:notation |
gptkb:SO_{n+1}(C)
gptkb:SO(n+1,_C) |
| gptkbp:relatedGroup |
gptkb:Lie_group
connected non-compact semisimple |
| gptkbp:relatedTo |
gptkb:Lie_algebra_so(n+1,_C)
gptkb:SO(n+1,_R) orthogonal group |
| gptkbp:bfsParent |
gptkb:SO(1,n)
|
| gptkbp:bfsLayer |
6
|