Statements (28)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
|
| gptkbp:actsOn |
vector space F^n
|
| gptkbp:centralTo |
set of scalar matrices with n-th roots of unity
|
| gptkbp:definedIn |
set of n x n matrices with determinant 1 over field F
|
| gptkbp:degree |
n
|
| gptkbp:determinant |
1
|
| gptkbp:field |
F
|
| gptkbp:fullName |
special linear group of degree n over field F
|
| gptkbp:generation |
elementary matrices
|
| gptkbp:hasSubgroup |
gptkb:GL(n,_F)
|
| https://www.w3.org/2000/01/rdf-schema#label |
SL(n, F)
|
| gptkbp:identityElement |
identity matrix
|
| gptkbp:importantFor |
gptkb:geometry
number theory representation theory algebraic group theory |
| gptkbp:isQuotientOf |
projective special linear group PSL(n, F)
|
| gptkbp:isSimple |
true for n > 2 and F not of small order
|
| gptkbp:notation |
gptkb:SL(n,_F)
|
| gptkbp:operator |
matrix multiplication
|
| gptkbp:order |
finite if F is finite
|
| gptkbp:relatedTo |
determinant function
linear transformations with determinant 1 |
| gptkbp:type |
gptkb:algebraic_geometry
Lie group (if F = R or C) |
| gptkbp:bfsParent |
gptkb:orthogonal_group
gptkb:Special_linear_group |
| gptkbp:bfsLayer |
5
|