Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:alsoKnownAs |
sl(n, F)
|
| gptkbp:associatedWith |
orthogonal group
|
| gptkbp:automorphismGroup |
gptkb:PGL(n,_F)
|
| gptkbp:basisFor |
matrix units with zero trace
|
| gptkbp:CartanSubalgebra |
diagonal traceless matrices
|
| gptkbp:centralTo |
trivial for n > 2
|
| gptkbp:consistsOf |
traceless n x n matrices
|
| gptkbp:definedIn |
field F
|
| gptkbp:dimensions |
n^2 - 1
|
| https://www.w3.org/2000/01/rdf-schema#label |
special linear Lie algebra
|
| gptkbp:isSimple |
n > 1 and char(F) = 0
|
| gptkbp:KillingForm |
non-degenerate for n > 1
|
| gptkbp:notation |
sl(n, F)
|
| gptkbp:relatedTo |
projective linear group
|
| gptkbp:structure |
[A,B] = AB - BA
|
| gptkbp:subclassOf |
gptkb:general_linear_Lie_algebra
|
| gptkbp:type |
A_{n-1}
|
| gptkbp:usedIn |
gptkb:theoretical_physics
differential geometry representation theory |
| gptkbp:bfsParent |
gptkb:orthogonal_group
|
| gptkbp:bfsLayer |
5
|