Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:automorphismGroup |
gptkb:PGL(n,_C)
|
| gptkbp:CartanSubalgebra |
diagonal trace zero matrices
|
| gptkbp:centralTo |
0
|
| gptkbp:defines |
the Lie algebra of n x 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:isomorphicTo |
gptkb:A_{n-1}_Lie_algebra
|
| gptkbp:isSimple |
true
|
| gptkbp:KillingForm |
non-degenerate
|
| gptkbp:rank |
n-1
|
| gptkbp:realForm |
gptkb:sl(n,_R)
su(n) |
| gptkbp:relatedGroup |
gptkb:SL(n,_C)
|
| gptkbp:representationTheory |
well-studied
|
| gptkbp:structureConstants |
[E_{ij}, E_{kl}] = δ_{jk}E_{il} - δ_{il}E_{kj}
|
| gptkbp:type |
A_{n-1}
|
| gptkbp:usedIn |
gptkb:theoretical_physics
differential geometry representation theory |
| gptkbp:bfsParent |
gptkb:semisimple_Lie_algebras
|
| gptkbp:bfsLayer |
6
|