Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:automorphismGroup |
gptkb:PGL(n,C)
|
| gptkbp:basisFor |
matrices with trace zero
|
| gptkbp:cartanSubalgebra |
diagonal trace zero matrices
|
| gptkbp:centralTo |
trivial
|
| gptkbp:defines |
the Lie algebra of n×n complex matrices with trace zero
|
| gptkbp:dimensions |
n^2 - 1
|
| gptkbp:field |
complex numbers
|
| gptkbp:fullName |
special linear Lie algebra over the complex numbers
|
| https://www.w3.org/2000/01/rdf-schema#label |
sl(n,C)
|
| gptkbp:isSemisimple |
true
|
| gptkbp:isSimple |
true
n > 1 |
| gptkbp:notation |
sl(n,ℂ)
|
| gptkbp:rank |
n-1
|
| gptkbp:realForm |
gptkb:sl(n,R)
|
| gptkbp:relatedGroup |
gptkb:SL(n,C)
|
| gptkbp:structure |
[A,B] = AB - BA
|
| gptkbp:type |
A_{n-1}
|
| gptkbp:universalEnvelopingAlgebra |
U(sl(n,C))
|
| gptkbp:bfsParent |
gptkb:special_linear_group_SL(n,C)
gptkb:classical_Lie_algebras |
| gptkbp:bfsLayer |
7
|