projective special linear group PSL(n, C)
GPTKB entity
Statements (41)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:Lie_group |
| gptkbp:actsOn |
complex projective space
|
| gptkbp:centerOfSL(n,_C) |
cyclic group of order n
|
| gptkbp:compact |
yes
|
| gptkbp:constructedAs |
SL(n, C) modulo center
|
| gptkbp:definedIn |
complex numbers
|
| gptkbp:dimensions |
n^2 - 1
|
| gptkbp:fullName |
Projective Special Linear Group over the complex numbers
|
| gptkbp:hasConnection |
yes
|
| gptkbp:hasSubgroup |
gptkb:PGL(n,_C)
|
| gptkbp:hasTrivialCenter |
yes
|
| https://www.w3.org/2000/01/rdf-schema#label |
projective special linear group PSL(n, C)
|
| gptkbp:isomorphicTo |
SL(n, C)/Z(SL(n, C))
|
| gptkbp:isPerfect |
yes (for n > 2)
|
| gptkbp:isQuotientOf |
gptkb:SL(n,_C)
SL(n, C) by its center |
| gptkbp:isSemisimple |
yes
|
| gptkbp:isSimple |
n > 2
yes (for n > 2) |
| gptkbp:nonAbelianFor |
n > 2
|
| gptkbp:notation |
gptkb:PSL(n,_C)
|
| gptkbp:order |
infinite (for n > 1)
|
| gptkbp:originatedIn |
gptkb:algebraic_geometry
differential geometry quantum mechanics representation theory theory of Lie groups theory of algebraic groups |
| gptkbp:relatedTo |
gptkb:projective_linear_group_PGL(n,_C)
|
| gptkbp:usedIn |
gptkb:geometry
modular forms number theory theory of Lie algebras theory of Riemann surfaces theory of algebraic groups theory of automorphic forms theory of algebraic curves theory of algebraic surfaces |
| gptkbp:bfsParent |
gptkb:special_linear_group_SL(n,_C)
|
| gptkbp:bfsLayer |
7
|