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Garside groups and Yang-Baxter equation

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arxiv 0912.4827 v3 pith:6ESBJPEM submitted 2009-12-24 math.GR math.RA

Garside groups and Yang-Baxter equation

Fabienne Chouraqui This is my paper
classification math.GR math.RA
keywords groupsgarsideequationsolutionsyang-baxteradmittingbraidedcertain
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We establish a one-to-one correspondence between a class of Garside groups admitting a certain presentation and the structure groups of non-degenerate, involutive and braided set-theoretical solutions of the quantum Yang-Baxter equation. We also characterize indecomposable solutions in terms of $\Delta$-pure Garside groups.

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    Lyubashenko solutions of the Yang-Baxter equation produce Markov processes equivalent to a twisted SSEP, whose stationary sectors are labeled exactly by a species profile and a total charge.