Statements (33)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:Lie_group |
| gptkbp:actsOn |
complex projective line
hyperbolic 3-space |
| gptkbp:centralTo |
{±I}
|
| gptkbp:compact |
true
|
| gptkbp:defines |
group of 2x2 complex matrices with determinant 1
|
| gptkbp:dimensions |
3
|
| gptkbp:field |
complex numbers
|
| gptkbp:fullName |
gptkb:Special_Linear_Group_of_2x2_Complex_Matrices
|
| gptkbp:hasConnection |
true
|
| gptkbp:hasSubgroup |
gptkb:SU(2)
gptkb:SL_2(R) |
| https://www.w3.org/2000/01/rdf-schema#label |
SL 2(C)
|
| gptkbp:isQuotientOf |
gptkb:PSL_2(C)
|
| gptkbp:isReductive |
true
|
| gptkbp:isSemisimple |
true
|
| gptkbp:isSimple |
true
|
| gptkbp:Lie_algebra |
sl_2(C)
|
| gptkbp:maximalCompactSubgroup |
gptkb:SU(2)
|
| gptkbp:notation |
gptkb:SL_2(C)
|
| gptkbp:rank |
1
|
| gptkbp:realForm |
gptkb:SL_2(R)
|
| gptkbp:relatedTo |
gptkb:Möbius_transformations
modular group |
| gptkbp:universalCover |
SO_3(C)
|
| gptkbp:usedIn |
gptkb:algebraic_geometry
gptkb:hyperbolic_geometry number theory quantum mechanics representation theory |
| gptkbp:bfsParent |
gptkb:SL_2(R)
|
| gptkbp:bfsLayer |
7
|