|
gptkbp:instanceOf
|
gptkb:group_of_people
|
|
gptkbp:actsOn
|
projective line
|
|
gptkbp:centralTo
|
{I, -I} (over fields of characteristic ≠ 2)
|
|
gptkbp:defines
|
The group of 2x2 matrices with determinant 1 over a field or ring
|
|
gptkbp:dimensions
|
3 (as Lie group over R or C)
|
|
gptkbp:fullName
|
gptkb:Special_Linear_Group_of_degree_2
|
|
gptkbp:hasConnection
|
yes (over R or C)
|
|
gptkbp:hasSubgroup
|
gptkb:GL(2)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SL(2)
|
|
gptkbp:isMatrixGroup
|
yes
|
|
gptkbp:isNonAbelian
|
yes
|
|
gptkbp:isPerfect
|
yes (for n ≥ 2, except in small characteristics)
|
|
gptkbp:isQuotientOf
|
gptkb:PSL(2)
|
|
gptkbp:isSimple
|
yes (for n ≥ 2, except in small characteristics)
|
|
gptkbp:Lie_algebra
|
sl(2)
|
|
gptkbp:notation
|
gptkb:SL(2)
gptkb:SL_2
|
|
gptkbp:order
|
infinite (over infinite fields)
(q^2-1)q (over finite field F_q)
|
|
gptkbp:relatedTo
|
gptkb:PSL(2)
gptkb:SL(n)
gptkb:GL(2)
|
|
gptkbp:type
|
gptkb:algebraic_geometry
gptkb:Lie_group
|
|
gptkbp:universalCover
|
yes (over R: universal cover is infinite cyclic cover)
|
|
gptkbp:usedIn
|
gptkb:algebraic_geometry
modular forms
number theory
quantum mechanics
representation theory
theory of modular curves
|
|
gptkbp:bfsParent
|
gptkb:SL2
|
|
gptkbp:bfsLayer
|
6
|