simple Lie algebra of type A n
GPTKB entity
Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:Cartan_subalgebra |
diagonal matrices (traceless)
|
| gptkbp:centralTo |
trivial
|
| gptkbp:class |
A_n
|
| gptkbp:dimensions |
n^2 + 2n
|
| gptkbp:Dynkin_diagram |
A_n
|
| gptkbp:example |
sl(n+1, C)
|
| gptkbp:field |
algebraically closed field
|
| gptkbp:heldBy |
highest weight representations
|
| https://www.w3.org/2000/01/rdf-schema#label |
simple Lie algebra of type A n
|
| gptkbp:isomorphicTo |
sl(n+1, K) for algebraically closed field K
|
| gptkbp:rank |
n
|
| gptkbp:relatedTo |
gptkb:special_linear_Lie_algebra
|
| gptkbp:structure_constants |
determined by commutator
|
| gptkbp:type |
gptkb:Lie_group
A_n |
| gptkbp:used_in |
gptkb:algebraic_geometry
gptkb:theoretical_physics differential geometry representation theory |
| gptkbp:Weyl_group |
gptkb:symmetric_group_S_{n+1}
|
| gptkbp:bfsParent |
gptkb:A_n_root_lattice
|
| gptkbp:bfsLayer |
6
|