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Let (X, r) be an involutive solution to the YBE. We know that its permutation group \(\mathcal {G}(X,r)\) has a natural structure of skew brace of abelian type. If \((Y,r')\) is a solution isomorphic to (X, r), then \(\mathcal {G}(Y,r')\cong \mathcal {G}(X,r)\) as skew braces. Thus the classification of the involutive solutions can be done in two steps:

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Involutive Solutions

  • 章节

  • 发表日期：

    2026年

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  • Ferran Cedó,
  • Leandro Vendramin

摘要

Let (X, r) be an involutive solution to the YBE. We know that its permutation group \(\mathcal {G}(X,r)\) has a natural structure of skew brace of abelian type. If \((Y,r')\) is a solution isomorphic to (X, r), then \(\mathcal {G}(Y,r')\cong \mathcal {G}(X,r)\) as skew braces. Thus the classification of the involutive solutions can be done in two steps: