Statements (30)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:alsoKnownAs |
gptkb:special_linear_Lie_algebra
|
| gptkbp:application |
differential geometry
particle physics quantum mechanics representation theory |
| gptkbp:CartanSubalgebraDimension |
n
|
| gptkbp:centralTo |
trivial
|
| gptkbp:classicalLieAlgebra |
true
|
| gptkbp:definingRelation |
[E_{i,j}, E_{j,k}] = E_{i,k}
[H_i, E_{j,k}] = (δ_{i,j} - δ_{i,k})E_{j,k} [H_i, H_j] = 0 |
| gptkbp:dimensions |
n^2 + 2n
|
| gptkbp:DynkinType |
A_n
|
| gptkbp:field |
complex numbers
|
| gptkbp:generation |
E_{i,j} (i ≠ j), H_i
|
| gptkbp:isSimple |
true
|
| gptkbp:KillingForm |
non-degenerate
|
| gptkbp:rank |
n
|
| gptkbp:realForm |
su(n+1)
|
| gptkbp:relatedGroup |
gptkb:SL(n+1)
|
| gptkbp:relatedTo |
gptkb:Young_tableaux
gptkb:Schur–Weyl_duality gptkb:Cartan_matrix_of_type_A_n representation of symmetric group |
| gptkbp:type |
gptkb:A_n_root_system
|
| gptkbp:Weyl_group |
gptkb:symmetric_group_S_{n+1}
|
| gptkbp:bfsParent |
gptkb:special_unitary_Lie_algebra
|
| gptkbp:bfsLayer |
7
|
| https://www.w3.org/2000/01/rdf-schema#label |
A n Lie algebra
|