projective linear group PGL(n, C)
GPTKB entity
Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebraic_geometry
gptkb:group_of_people gptkb:Lie_group |
| gptkbp:actsOn |
complex projective space
|
| gptkbp:appearsIn |
gptkb:algebraic_geometry
gptkb:geometry representation theory |
| gptkbp:centralTo |
trivial
|
| 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
|
| https://www.w3.org/2000/01/rdf-schema#label |
projective linear group PGL(n, C)
|
| gptkbp:isAlgebraicGroup |
true
|
| gptkbp:isLieGroupOfType |
A_{n-1}
|
| gptkbp:isMatrixGroup |
true
|
| gptkbp:isNonAbelian |
true
|
| gptkbp:isomorphicTo |
PSL(n, C) for n > 2
|
| gptkbp:isQuotientOf |
gptkb:general_linear_group_GL(n,_C)
center of GL(n, C) |
| gptkbp:isReductive |
true
|
| gptkbp:isSimple |
n > 2
|
| gptkbp:notation |
gptkb:PGL(n,_C)
|
| gptkbp:relatedTo |
gptkb:projective_special_linear_group_PSL(n,_C)
|
| gptkbp:bfsParent |
gptkb:projective_unitary_group_PU(n)
|
| gptkbp:bfsLayer |
7
|