Geodesic
An unpublished theorem of Manfred Schocker and the Patras-Reutenauer algebra
Journal of Algebraic Combinatorics, Tome 28 (2008) no. 1, pp. 25-42.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Patras, Reutenauer (J. Algebr. Comb. 16:301-314, [ 2002]) describe a subalgebra $\mathfrak A$ mathfrakA of the Malvenuto-Reutenauer algebra ?. Their paper contains several characteristic properties of this subalgebra. In an unpublished manuscript Manfred Schocker states without proof a theorem, providing two further characterizations of the Patras-Reutenauer algebra. In this paper we establish a slightly generalized version of Schocker's theorem, and give some applications. Finally we describe a derivation of the convolution algebra $\mathfrak A$ mathfrakA , which is a homomorphism for the inner product.
Keywords: keywords symmetric group algebras, reciprocity laws, Lie idempotents, Solomon's descent algebra 
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     author = {Blessenohl, Dieter},
     title = {An unpublished theorem of {Manfred} {Schocker} and the {Patras-Reutenauer} algebra},
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Blessenohl, Dieter. An unpublished theorem of Manfred Schocker and the Patras-Reutenauer algebra. Journal of Algebraic Combinatorics, Tome 28 (2008) no. 1, pp. 25-42. http://geodesic.mathdoc.fr/item/JAC_2008__28_1_a9/