Statements (36)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
|
| gptkbp:actsOn |
K^n
|
| gptkbp:application |
gptkb:algebraic_geometry
number theory representation theory linear algebra |
| gptkbp:centralTo |
scalar matrices
|
| gptkbp:definedIn |
group of n x n invertible matrices over field K
|
| gptkbp:determinant |
GL(n, K) → K^*
SL(n, K) |
| gptkbp:dimensions |
n^2 if K is R or C
|
| gptkbp:fullName |
general linear group of degree n over field K
|
| gptkbp:hasConnection |
true if K is algebraically closed
|
| gptkbp:hasDeterminantMap |
true
|
| gptkbp:hasSubgroup |
GL(m, K) for m > n
SL(n, K) |
| https://www.w3.org/2000/01/rdf-schema#label |
GL(n, K)
|
| gptkbp:identityElement |
identity matrix
matrix inverse |
| gptkbp:isAlgebraicGroup |
true
|
| gptkbp:isDiscrete |
true if K is finite field
|
| gptkbp:isMatrixGroup |
true
true if K = R or C |
| gptkbp:isNonAbelian |
true for n > 1
|
| gptkbp:isQuotientOf |
projective general linear group PGL(n, K)
|
| gptkbp:isReductive |
true
|
| gptkbp:isSimple |
false
|
| gptkbp:isTopologicalGroup |
true if K is topological field
|
| gptkbp:notation |
gptkb:GL(n,_K)
gptkb:GL_n(K) |
| gptkbp:operator |
matrix multiplication
|
| gptkbp:order |
finite if K is finite
product_{i=0}^{n-1} (|K|^n - |K|^i) if K is finite |
| gptkbp:relatedTo |
automorphism group of K^n
|
| gptkbp:bfsParent |
gptkb:Groupe_linéaire_général
|
| gptkbp:bfsLayer |
8
|