Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:Lie_group |
| gptkbp:actsOn |
projective space of dimension n
|
| gptkbp:centralTo |
cyclic group of order n+1
|
| gptkbp:definedIn |
group of (n+1)x(n+1) matrices with determinant 1
|
| gptkbp:dimensions |
(n+1)^2 - 1
|
| gptkbp:field |
usually over the complex numbers or real numbers
|
| gptkbp:fullName |
Special Linear Group of degree n+1
|
| gptkbp:hasConnection |
true
|
| gptkbp:hasSubgroup |
GL(n+1)
|
| https://www.w3.org/2000/01/rdf-schema#label |
SL(n+1)
|
| gptkbp:isAlgebraicGroup |
true
|
| gptkbp:isClassicalGroup |
true
|
| gptkbp:isNonAbelian |
true (for n+1 > 1)
|
| gptkbp:isReductive |
true
|
| gptkbp:isSemisimple |
true
|
| gptkbp:isSimple |
true (for n+1 > 1 and over algebraically closed fields)
|
| gptkbp:Lie_algebra |
sl(n+1)
|
| gptkbp:notation |
SL(n+1, F)
|
| gptkbp:relatedTo |
GL(n+1)
|
| gptkbp:usedIn |
gptkb:algebraic_geometry
differential geometry physics representation theory |
| gptkbp:bfsParent |
gptkb:A_n_Lie_algebra
gptkb:simple_Lie_algebra_sl(n+1) |
| gptkbp:bfsLayer |
8
|