Lie representations and an algebra containing Solomon's. (Q1863002)

In the paper under review, a Hopf algebra containing the descent algebra as a sub-Hopf algebra is studied. This Hopf algebra has the main algebraic properties of the descent algebra, and more: it is a sub-Hopf algebra of the direct sum of symmetric group algebras; it is closed under the corresponding inner product; it is cocommutative; it contains all Lie idempotents of the symmetric group algebras.