Statements (48)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
|
| gptkbp:application |
gptkb:algebraic_geometry
gptkb:geometry modular forms number theory quantum mechanics representation theory |
| gptkbp:centralTo |
{±I} (over algebraically closed field)
|
| gptkbp:defines |
group of 2x2 matrices with determinant 1 over a field
|
| gptkbp:dimensions |
3 (as Lie group over R or C)
|
| gptkbp:field |
algebraically closed fields
complex numbers finite fields real numbers arbitrary field |
| gptkbp:fullName |
gptkb:Special_Linear_Group_of_degree_2
|
| gptkbp:generation |
elementary matrices
|
| gptkbp:hasConnection |
yes (as Lie group)
yes (over algebraically closed fields) |
| gptkbp:hasSubgroup |
gptkb:GL_2
|
| https://www.w3.org/2000/01/rdf-schema#label |
SL 2
|
| gptkbp:isAlgebraicGroup |
yes
|
| gptkbp:isMatrixGroup |
yes
|
| gptkbp:isNonAbelian |
yes
|
| gptkbp:isPerfect |
yes
|
| gptkbp:isQuotientOf |
PSL_2
|
| gptkbp:isReductive |
yes
|
| gptkbp:isSemisimple |
yes
|
| gptkbp:isSimple |
no (over algebraically closed fields)
yes (for q > 3, over finite fields) |
| gptkbp:isSplit |
yes (over algebraically closed fields)
|
| gptkbp:notation |
gptkb:SL(2)
gptkb:SL_2 |
| gptkbp:order |
infinite (over infinite fields)
(q^3 - q) (over finite field F_q) |
| gptkbp:rank |
1
|
| gptkbp:relatedTo |
gptkb:GL_2
gptkb:hyperbolic_geometry automorphic forms modular group Lie algebra sl_2 Mobius transformations PSL_2 SU_2 |
| gptkbp:type |
A1
|
| gptkbp:universalCover |
yes
|
| gptkbp:bfsParent |
gptkb:SL(2)
|
| gptkbp:bfsLayer |
7
|