This article is cited in 21 papers

On descent algebras and twisted bialgebras

F. Patras^a, Ch. Reutenauer<sup>b

a</sup> Laboratoire de Mathématiques Jean Alexandre Dieudonné, Université de Nice Sophia Antipolis
^b Université de Montréal

Abstract: Bialgebras in the category of tensor species (twisted bialgebras) deserve a particular attention, in particular in view of applications to algebraic combinatorics. In order to study these bialgebras, a new class of descent algebras is introduced. The fine structure of Barratt's permutation bi-ring (the direct sum of the symmetric group algebras) is investigated in detail from this point of view, leading to the definition of an enveloping algebra structure on it.

Key words and phrases: Descent algebra, tensor species, symmetric group, permutation bi-ring, free Lie algebra.

MSC: Primary 16W30, 05E10; Secondary 17A30, 17B01, 17B35

Received: February 4, 2003

Language: English

DOI: 10.17323/1609-4514-2004-4-1-199-216

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