Various products of representative series
Publications mathématiques de Besançon. Algèbre et théorie des nombres (2025), pp. 115-144.

For factorizing and decomposing the representative (or rational) series, with coefficients in a commutative ring $A$ containing $\mathbb{Q}$, we examine various products (such as concatenation, shuffle, quasi-shuffle) defined on the free monoid which are such that their associated bialgebras are isomorphic to the Sweedler’s dual, for $A$ being a field $K$.

Pour factoriser et décomposer la série représentative (ou rationnelle) à coefficients dans un anneau commutatif $A$ contenant $\mathbb{Q}$, nous examinons divers produits (tels que concaténation, shuffle, quasi-shuffle) définis sur le monoïde libre qui sont tels que leurs bialgèbres associées sont isomorphes au dual de Sweedler, pour $A$ étant un corps $K$.

Publié le :
DOI : 10.5802/pmb.64
Keywords: noncommutative rational series, representative series, Sweedler’s dual
Mots-clés : Série rationnelle noncommutative, séries représentative, dual de Sweedler

V. C. Bui 1 ; V. Hoang Ngoc Minh 2 ; Q. H. Ngo 3 ; V. Nguyen Dinh 4

1 University of Sciences, Hue University, 77, Nguyen Hue, Hue, Viet Nam
2 Université de Lille, 1 Place Déliot, 59024 Lille, France
3 University of Science and Technology, 1 Dai Co Viet, Ha Noi, Viet Nam
4 Science and Technology University of Ha Noi, 18 Hoang Quoc Viet, Ha Noi, Viet Nam
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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V. C. Bui; V. Hoang Ngoc Minh; Q. H. Ngo; V. Nguyen Dinh. Various products of representative series. Publications mathématiques de Besançon. Algèbre et théorie des nombres (2025), pp. 115-144. doi : 10.5802/pmb.64. https://pmb.centre-mersenne.org/articles/10.5802/pmb.64/

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