Folding of set-theoretical solutions of the yang-baxter equation

Fabienne Chouraqui; Eddy Godelle

doi:10.1007/s10468-011-9288-0

Folding of set-theoretical solutions of the yang-baxter equation

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

Abstract

We establish a correspondence between the invariant subsets of a nondegenerate symmetric set-theoretical solution of the quantum Yang-Baxter equation and the parabolic subgroups of its structure group, equipped with its canonical Garside structure. Moreover, we introduce the notion of a foldable solution, which extends the one of a decomposable solution.

Original language	English
Pages (from-to)	1277-1290
Number of pages	14
Journal	Algebras and Representation Theory
Volume	15
Issue number	6
DOIs	https://doi.org/10.1007/s10468-011-9288-0
State	Published - Dec 2012
Externally published	Yes

Bibliographical note

Funding Information:
Fabienne Chouraqui and Eddy Godelle are partially supported by the Agence Nationale de la Recherche (projet Théorie de Garside, ANR-08-BLAN-0269-03). Fabienne Chouraqui is also supported by the Affdu-Elsevier fellowship.

Keywords

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

ASJC Scopus subject areas

General Mathematics

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10.1007/s10468-011-9288-0

Cite this

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abstract = "We establish a correspondence between the invariant subsets of a nondegenerate symmetric set-theoretical solution of the quantum Yang-Baxter equation and the parabolic subgroups of its structure group, equipped with its canonical Garside structure. Moreover, we introduce the notion of a foldable solution, which extends the one of a decomposable solution.",

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author = "Fabienne Chouraqui and Eddy Godelle",

note = "Funding Information: Fabienne Chouraqui and Eddy Godelle are partially supported by the Agence Nationale de la Recherche (projet Th{\'e}orie de Garside, ANR-08-BLAN-0269-03). Fabienne Chouraqui is also supported by the Affdu-Elsevier fellowship.",

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AU - Chouraqui, Fabienne

AU - Godelle, Eddy

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PY - 2012/12

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N2 - We establish a correspondence between the invariant subsets of a nondegenerate symmetric set-theoretical solution of the quantum Yang-Baxter equation and the parabolic subgroups of its structure group, equipped with its canonical Garside structure. Moreover, we introduce the notion of a foldable solution, which extends the one of a decomposable solution.

AB - We establish a correspondence between the invariant subsets of a nondegenerate symmetric set-theoretical solution of the quantum Yang-Baxter equation and the parabolic subgroups of its structure group, equipped with its canonical Garside structure. Moreover, we introduce the notion of a foldable solution, which extends the one of a decomposable solution.

KW - Folding

KW - Parabolic subgroups of Garside groups

KW - Set-theoretical solution of the quantum Yang-Baxter equation

UR - https://www.scopus.com/pages/publications/84897008692

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IS - 6

ER -

Folding of set-theoretical solutions of the yang-baxter equation

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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