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<p>As generalizations of skew left braces, weak left braces were introduced recently by Catino, Mazzotta, Miccoli and Stefanelli to study certain special degenerate set-theoretical solutions of the Yang–Baxter equation. In this note, as analogues of the notions of regular subgroups of holomorph of groups, Gamma functions on groups and affine and semi-affine structures on groups, we propose the notions of good inverse subsemigroups and Gamma functions associated to Clifford semigroups and affine structures on inverse semigroups, respectively, by which weak left braces are characterized. Some necessary examples are provided to illustrate the main results.</p>

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Some Characterizations of Weak Left Braces

  • 期刊论文

  • 发表日期：

    2026年8月1日

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  • Shoufeng Wang

摘要

As generalizations of skew left braces, weak left braces were introduced recently by Catino, Mazzotta, Miccoli and Stefanelli to study certain special degenerate set-theoretical solutions of the Yang–Baxter equation. In this note, as analogues of the notions of regular subgroups of holomorph of groups, Gamma functions on groups and affine and semi-affine structures on groups, we propose the notions of good inverse subsemigroups and Gamma functions associated to Clifford semigroups and affine structures on inverse semigroups, respectively, by which weak left braces are characterized. Some necessary examples are provided to illustrate the main results.