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# Mathematical Physics

# Title: Set theoretic Yang-Baxter equation, braces and Drinfeld twists

(Submitted on 26 Feb 2021 (v1), last revised 22 Sep 2021 (this version, v3))

Abstract: We consider involutive, non-degenerate, finite set theoretic solutions of the Yang-Baxter equation. Such solutions can be always obtained using certain algebraic structures that generalize nil potent rings called braces. Our main aim here is to express such solutions in terms of admissible Drinfeld twists substantially extending recent preliminary results. We first identify the generic form of the twists associated to set theoretic solutions and we show that these twists are admissible, i.e. they satisfy a certain co-cycle condition. These findings are also valid for Baxterized solutions of the Yang-Baxter equation constructed from the set theoretical ones.

## Submission history

From: Anastasia Doikou [view email]**[v1]**Fri, 26 Feb 2021 16:57:20 GMT (22kb)

**[v2]**Mon, 15 Mar 2021 14:23:33 GMT (22kb)

**[v3]**Wed, 22 Sep 2021 07:08:31 GMT (22kb)

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