Growth function for a class of monoids

Marie Albenque; Philippe Nadeau

Growth function for a class of monoids

Marie Albenque
, Philippe Nadeau

Université Paris 7
University of Vienna

Résultats de recherche: Contribution à une conférence › Papier › Revue par des pairs

Résumé

In this article we study a class of monoids that includes Garside monoids, and give a simple combinatorial proof of a formula for the formal sum of all elements of the monoid. This leads to a formula for the growth function of the monoid in the homogeneous case, and can also be lifted to a resolution of the monoid algebra. These results are then applied to known monoids related to Coxeter systems: we give the growth function of the Artin-Tits monoids, and do the same for the dual braid monoids. In this last case we show that the monoid algebras of the dual braid monoids of type A and B are Koszul algebras.

langue originale	Anglais
Pages	25-38
Nombre de pages	14
état	Publié - 1 déc. 2009
Modification externe	Oui
Evénement	21st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'09 - Linz, Autriche Durée: 20 juil. 2009 → 24 juil. 2009

Une conférence

Une conférence	21st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'09
Pays/Territoire	Autriche
La ville	Linz
période	20/07/09 → 24/07/09

Contient cette citation

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title = "Growth function for a class of monoids",

abstract = "In this article we study a class of monoids that includes Garside monoids, and give a simple combinatorial proof of a formula for the formal sum of all elements of the monoid. This leads to a formula for the growth function of the monoid in the homogeneous case, and can also be lifted to a resolution of the monoid algebra. These results are then applied to known monoids related to Coxeter systems: we give the growth function of the Artin-Tits monoids, and do the same for the dual braid monoids. In this last case we show that the monoid algebras of the dual braid monoids of type A and B are Koszul algebras.",

keywords = "Garside group, Growth function, Koszul algebra, Monoid, Resolution",

author = "Marie Albenque and Philippe Nadeau",

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T1 - Growth function for a class of monoids

AU - Albenque, Marie

AU - Nadeau, Philippe

PY - 2009/12/1

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N2 - In this article we study a class of monoids that includes Garside monoids, and give a simple combinatorial proof of a formula for the formal sum of all elements of the monoid. This leads to a formula for the growth function of the monoid in the homogeneous case, and can also be lifted to a resolution of the monoid algebra. These results are then applied to known monoids related to Coxeter systems: we give the growth function of the Artin-Tits monoids, and do the same for the dual braid monoids. In this last case we show that the monoid algebras of the dual braid monoids of type A and B are Koszul algebras.

AB - In this article we study a class of monoids that includes Garside monoids, and give a simple combinatorial proof of a formula for the formal sum of all elements of the monoid. This leads to a formula for the growth function of the monoid in the homogeneous case, and can also be lifted to a resolution of the monoid algebra. These results are then applied to known monoids related to Coxeter systems: we give the growth function of the Artin-Tits monoids, and do the same for the dual braid monoids. In this last case we show that the monoid algebras of the dual braid monoids of type A and B are Koszul algebras.

KW - Garside group

KW - Growth function

KW - Koszul algebra

KW - Monoid

KW - Resolution

M3 - Paper

AN - SCOPUS:84860455180

SP - 25

EP - 38

T2 - 21st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'09

Y2 - 20 July 2009 through 24 July 2009

ER -

Growth function for a class of monoids

Résumé

Une conférence

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