Decomposition theorems for involutive solutions to the Yang-Baxter equation

Abstract

Motivated by the proof of Rump of a conjecture of Gateva-Ivanova on the decomposability of square-free solutions to the Yang-Baxter equation, we present several other decomposability theorems based on the cycle structure of a certain permutation associated with the solution.

arXiv comment10 pages. Accepted for publication in Int. Math. Res. Not. IMRN

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Cited by in corpus (2)

• Skew braces: a brief survey
• Multinomial expansion and Nichols algebras associated to non-degenerate involutive solutions of the Yang-Baxter equation