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 |
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Pages (from-to) | 1277-1290 |
Number of pages | 14 |
Journal | Algebras and Representation Theory |
Volume | 15 |
Issue number | 6 |
DOIs | |
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