Finite quotients of groups of I-type

Fabienne Chouraqui; Eddy Godelle

doi:10.1016/j.aim.2014.02.009

Finite quotients of groups of I-type

Research output: Contribution to journal › Article › peer-review

Abstract

To every group of I-type, we associate a finite quotient group that plays the role that Coxeter groups play for Artin-Tits groups. Since groups of I-type are examples of Garside groups, this answers a question of D. Bessis in the particular case of groups of I-type. Groups of I-type are related to finite set-theoretical solutions of the Yang-Baxter equation. So, our result provides a new tool to attack the problem of the classification of finite set-theoretical solutions of the Yang-Baxter equation.

Original language	English
Pages (from-to)	46-68
Number of pages	23
Journal	Advances in Mathematics
Volume	258
DOIs	https://doi.org/10.1016/j.aim.2014.02.009
State	Published - 20 Jun 2014

Bibliographical note

Funding Information:
Both authors are partially supported by the Agence Nationale de la Recherche (projet Théorie de Garside, ANR-08-BLAN-0269-03 ). The first author was supported by the Israel Science Foundation (n o 580/07 ).

Keywords

Garside groups
Set-theoretical solution of the quantum Yang-Baxter equation

ASJC Scopus subject areas

Mathematics (all)

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10.1016/j.aim.2014.02.009

Cite this

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AU - Godelle, Eddy

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N2 - To every group of I-type, we associate a finite quotient group that plays the role that Coxeter groups play for Artin-Tits groups. Since groups of I-type are examples of Garside groups, this answers a question of D. Bessis in the particular case of groups of I-type. Groups of I-type are related to finite set-theoretical solutions of the Yang-Baxter equation. So, our result provides a new tool to attack the problem of the classification of finite set-theoretical solutions of the Yang-Baxter equation.

AB - To every group of I-type, we associate a finite quotient group that plays the role that Coxeter groups play for Artin-Tits groups. Since groups of I-type are examples of Garside groups, this answers a question of D. Bessis in the particular case of groups of I-type. Groups of I-type are related to finite set-theoretical solutions of the Yang-Baxter equation. So, our result provides a new tool to attack the problem of the classification of finite set-theoretical solutions of the Yang-Baxter equation.

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JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Finite quotients of groups of I-type

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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