A n Lie algebra

URI: https://gptkb.org/entity/A_n_Lie_algebra
GPTKB entity
Statements (31)
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
https://www.w3.org/2000/01/rdf-schema#label A n Lie algebra
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
gptkb:D_n_Lie_algebra
gptkbp:bfsLayer 7