GL(n, C) modulo scalar matrices
GPTKB entity
Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
|
| gptkbp:actsOn |
complex projective space
projective space of dimension n-1 |
| gptkbp:alsoKnownAs |
projective general linear group
|
| gptkbp:centerOfGL(n,_C) |
scalar matrices
|
| gptkbp:constructedAs |
GL(n, C) / (C^* I)
|
| gptkbp:contains |
gptkb:PSL(n,_C)
|
| gptkbp:dimensions |
n^2 - 1
|
| gptkbp:field |
complex numbers
|
| https://www.w3.org/2000/01/rdf-schema#label |
GL(n, C) modulo scalar matrices
|
| gptkbp:isAlgebraicGroup |
true
|
| gptkbp:isMatrixGroup |
true
|
| gptkbp:isomorphicTo |
Aut(P^{n-1}(C))
|
| gptkbp:isQuotientOf |
gptkb:GL(n,_C)
center of GL(n, C) |
| gptkbp:isSimple |
n > 2
|
| gptkbp:relatedTo |
projective linear transformations
|
| gptkbp:standardNotation |
gptkb:PGL(n,_C)
|
| gptkbp:usedIn |
gptkb:algebraic_geometry
gptkb:geometry representation theory |
| gptkbp:bfsParent |
gptkb:PGL(n,_C)
gptkb:projective_linear_group_PGL(n,_C) |
| gptkbp:bfsLayer |
8
|