L'algebre de Lie des transpositions

الأصل · EN

For any n ≥ 3 we obtain the decomposition in simple factors of the Lie subalgebra of the group algebra of the symmetric group on n letters generated by the transpositions. This enables us to determine the algebraic hull of the braid group ₙ and of several of its subgroups inside the representations of the Iwahori-Hecke algebra of type A.