Statements (30)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebraic_geometry
gptkb:group_of_people gptkb:Lie_group |
| gptkbp:actsOn |
complex projective space
|
| gptkbp:automorphismGroup |
complex projective space
|
| gptkbp:centralTo |
trivial
|
| gptkbp:compact |
true
|
| gptkbp:constructedAs |
gptkb:GL(n,_C)_modulo_scalar_matrices
|
| gptkbp:definedIn |
complex numbers
|
| gptkbp:dimensions |
n^2 - 1
|
| gptkbp:fullName |
gptkb:projective_general_linear_group_over_the_complex_numbers
|
| gptkbp:hasConnection |
true
|
| gptkbp:hasSubgroup |
gptkb:projective_symplectic_group
gptkb:PSL(n,_C) gptkb:projective_orthogonal_group |
| https://www.w3.org/2000/01/rdf-schema#label |
PGL(n, C)
|
| gptkbp:isAlgebraicGroup |
C
true |
| gptkbp:isLieGroupOver |
C
|
| gptkbp:isMatrixGroup |
true
|
| gptkbp:isQuotientOf |
gptkb:GL(n,_C)
C* (nonzero complex numbers) GL(n, C) / C* |
| gptkbp:isReductive |
true
|
| gptkbp:isSimple |
n > 2
|
| gptkbp:notation |
gptkb:PGL(n,_C)
|
| gptkbp:relatedTo |
gptkb:PSL(n,_C)
|
| gptkbp:bfsParent |
gptkb:projective_unitary_group_PU(n)
gptkb:sl(n,_C) |
| gptkbp:bfsLayer |
7
|