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arXiv · 2110.03988

A note on set theoretical solutions of the Yang-Baxter equation with trivial retraction

Pablo Zadunaisky
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Abstract

We show that every finite non-degenerate set theoretical solution to the YBE whose retraction is a flip linearizes to a twist of the flip solution by roots of unity. This generalizes a result of Gateva-Ivanova and Majid. To prove the result we use a new invariant associated to a solution, its Lie algebra. We show also that a solution retracts to a flip solution if and only if its Lie algebra is abelian.

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Pablo Zadunaisky. 2021-10-08. A note on set theoretical solutions of the Yang-Baxter equation with trivial retraction. https://arxiv.org/abs/2110.03988

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