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Moscow Mathematical Journal, 2004, Volume 4, Number 1, Pages 199–216
DOI: https://doi.org/10.17323/1609-4514-2004-4-1-199-216 (Mi mmj148) 		 
This article is cited in 19 scientific papers (total in 19 papers)

On descent algebras and twisted bialgebras

F. Patrasa, Ch. Reutenauerb

a Laboratoire de Mathématiques Jean Alexandre Dieudonné, Université de Nice Sophia Antipolis
b Université de Montréal
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DOI: https://doi.org/10.17323/1609-4514-2004-4-1-199-216
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.
Received: February 4, 2003
Bibliographic databases:
MSC: Primary 16W30, 05E10; Secondary 17A30, 17B01, 17B35
Language: English
Citation: F. Patras, Ch. Reutenauer, “On descent algebras and twisted bialgebras”, Mosc. Math. J., 4:1 (2004), 199–216
Citation in format AMSBIB
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\by F.~Patras, Ch.~Reutenauer
\paper On descent algebras and twisted bialgebras
\jour Mosc. Math.~J.
\yr 2004
\vol 4
\issue 1
\pages 199--216
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2074989}
\zmath{https://zbmath.org/?q=an:1103.16026}
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