Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Lie algebra type
|
| gptkbp:appearsIn |
classification of simple Lie algebras
|
| gptkbp:Cartan_matrix |
A_n Cartan matrix
|
| gptkbp:correspondsTo |
gptkb:special_linear_Lie_algebra
|
| gptkbp:dimensions |
n^2+2n
|
| gptkbp:Dynkin_diagram |
A_n
|
| gptkbp:firstInCartanClassification |
yes
|
| gptkbp:fundamentalGroup |
Z/(n+1)Z
|
| https://www.w3.org/2000/01/rdf-schema#label |
Lie type A n
|
| gptkbp:overComplexNumbers |
sl(n+1,C)
|
| gptkbp:rank |
n
|
| gptkbp:realForm |
su(n+1)
sl(n+1,R) |
| gptkbp:relatedGroup |
special linear group SL(n+1)
|
| gptkbp:simpleLieAlgebra |
sl(n+1)
|
| gptkbp:type |
gptkb:A_n_root_system
|
| gptkbp:usedIn |
gptkb:algebraic_geometry
gptkb:theoretical_physics differential geometry representation theory |
| gptkbp:Weyl_group |
gptkb:symmetric_group_S_{n+1}
|
| gptkbp:bfsParent |
gptkb:Lie_type_D_n
|
| gptkbp:bfsLayer |
8
|