Statements (51)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
|
| gptkbp:actsOn |
2-dimensional vector space
|
| gptkbp:centralTo |
scalar matrices
|
| gptkbp:containsElement |
invertible 2x2 matrices
|
| gptkbp:describes |
group of all invertible 2x2 matrices over a field
|
| gptkbp:determinant |
nonzero
|
| gptkbp:fieldParameter |
field F
|
| gptkbp:fullName |
general linear group of degree 2
|
| gptkbp:hasSubgroup |
gptkb:SL(2)
Borel subgroup upper triangular matrices GL(n) for n>2 diagonal matrices diagonal subgroup unipotent subgroup |
| https://www.w3.org/2000/01/rdf-schema#label |
GL(2)
|
| gptkbp:identityElement |
matrix inverse
2x2 identity matrix |
| gptkbp:isAlgebraicGroup |
true
|
| gptkbp:isConnectedGroup |
true
|
| gptkbp:isMatrixGroup |
true
true (over R or C) |
| gptkbp:isNonAbelian |
true
|
| gptkbp:isQuotientOf |
gptkb:PGL(2)
|
| gptkbp:isReductive |
true
|
| gptkbp:isSimple |
false
|
| gptkbp:matrixSize |
2x2
|
| gptkbp:notation |
gptkb:GL_2
gptkb:GL(2) |
| gptkbp:operator |
matrix multiplication
|
| gptkbp:order |
infinite (over infinite fields)
(q^2-1)(q^2-q) (over finite field F_q) |
| gptkbp:relatedTo |
gptkb:Lie_groups
group theory representation theory algebraic groups orthogonal group group representations projective linear group determinant map |
| gptkbp:usedIn |
gptkb:algebraic_geometry
coding theory cryptography modular forms number theory representation theory linear algebra automorphic forms |
| gptkbp:bfsParent |
gptkb:Base_change_for_GL(2)
gptkb:Ramanujan_conjecture |
| gptkbp:bfsLayer |
6
|