Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:alsoKnownAs |
gptkb:special_linear_Lie_algebra
|
| gptkbp:appearsIn |
gptkb:theoretical_physics
differential geometry representation theory theory of algebraic groups |
| gptkbp:automorphismGroup |
PGL(n+1)
|
| gptkbp:CartanSubalgebraDimension |
n
|
| gptkbp:centralTo |
trivial
|
| gptkbp:class |
gptkb:classical_Lie_algebra
|
| gptkbp:defines |
Lie algebra of (n+1)x(n+1) matrices with trace zero
|
| gptkbp:dimensions |
(n+1)^2 - 1
|
| gptkbp:highestWeightRepresentation |
fundamental representations of type A_n
|
| https://www.w3.org/2000/01/rdf-schema#label |
simple Lie algebra sl(n+1)
|
| gptkbp:isSemisimple |
true
|
| gptkbp:isSimple |
true
|
| gptkbp:KillingForm |
non-degenerate
|
| gptkbp:notation |
sl(n+1)
|
| gptkbp:rank |
gptkb:Field
complex numbers n real numbers |
| gptkbp:relatedGroup |
gptkb:SL(n+1)
PSL(n+1) |
| gptkbp:type |
type A_n
|
| gptkbp:bfsParent |
gptkb:A_n^{(1)}
|
| gptkbp:bfsLayer |
7
|