Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:automorphismGroup |
gptkb:PGL(n,C)
|
| gptkbp:basisFor |
matrix units E_{ij}
|
| gptkbp:CartanSubalgebra |
diagonal matrices
|
| gptkbp:centerDimension |
1
|
| gptkbp:centralTo |
scalar matrices
|
| gptkbp:commutatorSubalgebra |
gptkb:sl(n,C)
|
| gptkbp:contains |
gptkb:sl(n,C)
|
| gptkbp:dimensions |
n^2
|
| gptkbp:directSum |
sl(n,C) and 1-dimensional center
|
| gptkbp:envelopingAlgebra |
universal enveloping algebra of gl(n,C)
|
| gptkbp:field |
complex numbers
|
| gptkbp:fullName |
general linear Lie algebra of n by n complex matrices
|
| https://www.w3.org/2000/01/rdf-schema#label |
gl(n,C)
|
| gptkbp:isReductive |
true
|
| gptkbp:isSemisimple |
false
|
| gptkbp:isSimple |
false
|
| gptkbp:KillingForm |
degenerate
|
| gptkbp:overAlgebraicallyClosedField |
yes
|
| gptkbp:realForm |
gl(n,R)
|
| gptkbp:relatedGroup |
gptkb:GL(n,C)
|
| gptkbp:represents |
standard representation on C^n
|
| gptkbp:structureConstants |
matrix commutator
|
| gptkbp:type |
type A_{n-1}
|
| gptkbp:weightLattice |
Z^n
|
| gptkbp:bfsParent |
gptkb:general_linear_group_GL(n,C)
|
| gptkbp:bfsLayer |
7
|