Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:Lie_group |
| gptkbp:actsOn |
vector spaces of dimension N
|
| gptkbp:centralTo |
scalar matrices with N-th roots of unity
|
| gptkbp:definedIn |
group of N x N matrices with determinant 1
|
| gptkbp:dimensions |
N^2 - 1
|
| gptkbp:field |
usually over real or complex numbers
|
| gptkbp:generation |
elementary matrices with determinant 1
|
| gptkbp:hasConnection |
true (over real or complex numbers)
|
| gptkbp:hasSubgroup |
general linear group GL(N)
|
| https://www.w3.org/2000/01/rdf-schema#label |
special linear group SL(N)
|
| gptkbp:importantFor |
gptkb:algebraic_geometry
differential geometry physics representation theory |
| gptkbp:isNonAbelian |
true for N > 2
|
| gptkbp:isSimple |
N >= 2 (over algebraically closed fields, except N=2 in characteristic 2)
|
| gptkbp:notation |
SL(N)
|
| gptkbp:order |
infinite (for infinite fields)
|
| gptkbp:relatedTo |
projective special linear group PSL(N)
|
| gptkbp:bfsParent |
gptkb:SU(N)_algebra
|
| gptkbp:bfsLayer |
7
|