projective general linear group PGL(n,C)
GPTKB entity
Statements (26)
| 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:automorphismGroup |
gptkb:geometry
|
| gptkbp:centralTo |
trivial
|
| gptkbp:compact |
true
|
| gptkbp:constructedAs |
GL(n,C) modulo scalar matrices
|
| gptkbp:definedIn |
complex numbers
|
| gptkbp:dimensions |
n^2 - 1
|
| gptkbp:hasConnection |
true
|
| gptkbp:hasSubgroup |
gptkb:projective_special_linear_group_PSL(n,C)
|
| https://www.w3.org/2000/01/rdf-schema#label |
projective general linear group PGL(n,C)
|
| gptkbp:isAlgebraicGroup |
C
|
| gptkbp:isQuotientOf |
gptkb:GL(n,C)
C^* (nonzero complex scalars) SL(n,C) by center |
| gptkbp:isReductive |
true
|
| gptkbp:isSimple |
n > 2
|
| gptkbp:notation |
gptkb:PGL(n,C)
|
| gptkbp:relatedTo |
gptkb:general_linear_group_GL(n,C)
|
| gptkbp:bfsParent |
gptkb:general_linear_group_GL(n,C)
|
| gptkbp:bfsLayer |
7
|