Special Linear Group of degree 2
GPTKB entity
Statements (26)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
|
| gptkbp:abbreviation |
gptkb:SL(2)
|
| gptkbp:application |
gptkb:geometry
number theory representation theory theory of Lie groups |
| gptkbp:centralTo |
scalar matrices with determinant 1
|
| gptkbp:defines |
group of 2x2 matrices with determinant 1
|
| gptkbp:field |
can be defined over any field
|
| gptkbp:generation |
elementary matrices
|
| gptkbp:hasSubgroup |
gptkb:General_Linear_Group_of_degree_2
|
| https://www.w3.org/2000/01/rdf-schema#label |
Special Linear Group of degree 2
|
| gptkbp:identityElement |
2x2 identity matrix
|
| gptkbp:important_subgroup |
gptkb:Projective_Special_Linear_Group_of_degree_2
|
| gptkbp:inverse_element |
matrix inverse
|
| gptkbp:isSimple |
true for most fields except small ones
|
| gptkbp:notation |
gptkb:SL(2,_F)
|
| gptkbp:operator |
matrix multiplication
|
| gptkbp:order |
(q^2-1)q for finite field of order q
infinite over infinite fields |
| gptkbp:relatedTo |
gptkb:GL(2,_F)
gptkb:PSL(2,_F) modular group determinant function |
| gptkbp:bfsParent |
gptkb:SL2
|
| gptkbp:bfsLayer |
6
|