Abstract
We establish a correspondence between the invariant subsets of a non-degenerate 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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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.
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Chouraqui, F., Godelle, E. Folding of Set-Theoretical Solutions of the Yang–Baxter Equation. Algebr Represent Theor 15, 1277–1290 (2012). https://doi.org/10.1007/s10468-011-9288-0
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DOI: https://doi.org/10.1007/s10468-011-9288-0
Keywords
- Set-theoretical solution of the quantum Yang–Baxter equation
- Parabolic subgroups of Garside groups
- Folding