|
gptkbp:instanceOf
|
gptkb:Lie_group
|
|
gptkbp:actsOn
|
C^{n+1}
|
|
gptkbp:centralTo
|
{I, -I} (for n+1 even)
{I} (for n+1 odd)
|
|
gptkbp:compact
|
false
true
|
|
gptkbp:definedIn
|
determinant 1 and preserving symmetric bilinear form
|
|
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
|
C
|
|
gptkbp:fullName
|
Special Orthogonal Group of degree n+1 over the complex numbers
|
|
gptkbp:hasConnection
|
false
true
|
|
gptkbp:hasSubgroup
|
GL_{n+1}(C)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SO {n+1}(C)
|
|
gptkbp:isAlgebraicGroup
|
true
|
|
gptkbp:isClassicalGroup
|
true
|
|
gptkbp:isConnectedFor
|
n+1 >= 2
|
|
gptkbp:isMatrixGroup
|
true
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isReductive
|
true
|
|
gptkbp:isSemisimple
|
true
|
|
gptkbp:isSimple
|
true
n+1 >= 3
|
|
gptkbp:Lie_algebra
|
so_{n+1}(C)
|
|
gptkbp:notation
|
gptkb:SO(n+1,_C)
|
|
gptkbp:relatedTo
|
orthogonal group
|
|
gptkbp:type
|
D_k (for n+1=2k), B_k (for n+1=2k+1)
|
|
gptkbp:universalCover
|
Spin_{n+1}(C)
|
|
gptkbp:bfsParent
|
gptkb:SO(n+1,_C)
|
|
gptkbp:bfsLayer
|
7
|