Dieter Blessenohl:

An Unpublished Theorem of Manfred Schocker and the Patras-Reutenauer Algebra

In [PR02] FrŽedŽeric Patras and Christophe Reutenauer describe a subalgebra A of the Malvenuto-Reutenauer algebra P. 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 In an unpublished manuscript Manfred Schocker states without proof a theorem, providing two further characterizations of the Patras-Reutenauer algebra.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 A, which is a homomorphism for the inner product.

Keywords: Symmetric group algebras, reciprocity laws, Lie idempotents, Solomon's descent algebra

Mail an Jens Burmeister

[Thu Feb 19 18:56:37 2009]

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