Statements (29)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:Lie_group |
| gptkbp:application |
gptkb:algebraic_geometry
differential geometry physics representation theory |
| gptkbp:centralTo |
scalar matrices with nonzero complex entries
|
| gptkbp:connects |
true
|
| gptkbp:containsElement |
invertible 2n x 2n complex matrices
|
| gptkbp:determinant |
GL(2n, C) → C*
|
| gptkbp:dimensions |
(2n)^2
|
| gptkbp:field |
complex numbers
|
| gptkbp:fullName |
General Linear Group of degree 2n over the complex numbers
|
| gptkbp:hasSubgroup |
gptkb:Sp(2n,_C)
U(2n) O(2n, C) SL(2n, C) |
| gptkbp:homomorphism |
determinant
|
| https://www.w3.org/2000/01/rdf-schema#label |
GL(2n, C)
|
| gptkbp:identityElement |
2n x 2n identity matrix
|
| gptkbp:isQuotientOf |
PGL(2n, C)
|
| gptkbp:isSimple |
false
|
| gptkbp:Lie_algebra |
gl(2n, C)
|
| gptkbp:maximalCompactSubgroup |
U(2n)
|
| gptkbp:operator |
matrix multiplication
|
| gptkbp:realForm |
GL(2n, R)
|
| gptkbp:relatedGroup |
non-abelian
|
| gptkbp:bfsParent |
gptkb:USp(2n)
|
| gptkbp:bfsLayer |
7
|