Folding of set-theoretical solutions of the Yang-Baxter equation

Details Folding of set-theoretical solutions of the Yang-Baxter equation Folding of set-theoretical solutions of the Yang-Baxter equation

2010-09-17

arxiv.org/abs/1009.3342v1

Mathematics

Group Theory

Scientific paper

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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