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Decomposition Theorems for Involutive Solutions to the Yang–Baxter Equation

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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… Click to show full 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.

Keywords: decomposition theorems; solutions yang; baxter equation; yang baxter; theorems involutive

Journal Title: International Mathematics Research Notices
Year Published: 2021

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