"Set-theoretical" solutions of the quantum Yang-Baxter equation and a class of Garside groups

Details "Set-theoretical" solutions of the quantum Yang-Baxter equation and a class of Garside groups "Set-theoretical" solutions of the quantum Yang-Baxter equation and a class of Garside groups

2008-11-25

arxiv.org/abs/0811.4064v2

Mathematics

Group Theory

Scientific paper

We establish a one-to-one correspondence between structure groups of
non-degenerate, involutive and braided "set-theoretical" solutions of the
quantum Yang-Baxter equation and Garside groups with a certain presentation.
Moreover, we show that the solution is indecomposable if and only if its
structure group is a $\Delta-$pure Garside group.

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