L'algebre de Lie des transpositions
Abstract
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.
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