Statements (51)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
|
| gptkbp:actsOn |
Q^2
|
| gptkbp:centralTo |
scalar matrices over Q
|
| gptkbp:contains |
gptkb:SL_2(Q)
permutation matrices diagonal matrices over Q lower triangular invertible matrices over Q scalar matrices over Q upper triangular invertible matrices over Q |
| gptkbp:defines |
the group of all 2x2 invertible matrices with entries in Q under matrix multiplication
|
| gptkbp:determinant |
gptkb:SL_2(Q)
|
| gptkbp:dimensions |
4
|
| gptkbp:field |
gptkb:Q
|
| gptkbp:fieldCharacteristic |
0
|
| gptkbp:fullName |
general linear group of 2x2 invertible matrices over the rationals
|
| gptkbp:hasConnection |
true
|
| gptkbp:hasSubgroup |
GL_2(C)
GL_2(R) |
| gptkbp:homomorphism |
determinant: GL_2(Q) → Q^*
|
| https://www.w3.org/2000/01/rdf-schema#label |
GL 2(Q)
|
| gptkbp:identityElement |
matrix inverse
2x2 identity matrix |
| gptkbp:isAlgebraicGroup |
true
|
| gptkbp:isCountable |
true
|
| gptkbp:isFinite |
false
|
| gptkbp:isNilpotent |
false
|
| gptkbp:isNonAbelian |
true
|
| gptkbp:isPerfect |
false
|
| gptkbp:isQuotientOf |
PGL_2(Q)
|
| gptkbp:isReductive |
true
|
| gptkbp:isSimple |
false
|
| gptkbp:isSolvable |
false
|
| gptkbp:notation |
gptkb:GL_2(Q)
GL(2,Q) |
| gptkbp:operator |
matrix multiplication
|
| gptkbp:order |
infinite
|
| gptkbp:relatedGroup |
gptkb:group_of_people
gptkb:Lie_group orthogonal group |
| gptkbp:relatedTo |
gptkb:algebraic_geometry
modular forms number theory representation theory algebraic groups automorphic forms Galois representations group cohomology group actions determinant map |
| gptkbp:bfsParent |
gptkb:SL_2(Q)
|
| gptkbp:bfsLayer |
8
|