Abstract Using the theory of cycle sets and braces, non-degenerate indecomposable involutive set-theoretic solutions to the Yang–Baxter equation are classified in terms of their universal coverings and their fundamental group. The universal coverings are characterized as braces with an adjoint orbit generating the additive group. Using this description, all coverings of non-degenerate indecomposable cycle sets are classified. The method is illustrated by examples.

中文翻译：

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杨-巴克斯特方程不可分解对合集合论解的分类

摘要 利用循环集和大括号理论，杨-巴克斯特方程的非退化不可分解对合集合论解根据其普遍覆盖和基本群进行分类。通用覆盖物的特征是带有产生可加组的伴随轨道的支架。使用此描述，对非退化不可分解循环集的所有覆盖进行分类。该方法通过示例进行说明。