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<p>We introduce a family of inverse monoids and refer to them as inverse Artin monoids associated to Boolean reflection monoids, and give their partial braid realizations. The construction is the same spirit as the one of inverse braid monoids with respect to symmetric inverse monoids. Inverse Artin monoids recover Easdown–Lavers’ inverse braid monoid (in type <i>A</i>) and the inverse braid monoid of type <i>B</i> in the sense of Vershinin (in type <i>B</i>). We obtain a family of presentations of inverse Artin monoids of type <i>A</i> by cluster mutations.</p>

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Inverse Artin monoids and partial braid realizations

  • 期刊论文

  • 发表日期：

    2025年7月16日

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  • Bing Duan

摘要

We introduce a family of inverse monoids and refer to them as inverse Artin monoids associated to Boolean reflection monoids, and give their partial braid realizations. The construction is the same spirit as the one of inverse braid monoids with respect to symmetric inverse monoids. Inverse Artin monoids recover Easdown–Lavers’ inverse braid monoid (in type A) and the inverse braid monoid of type B in the sense of Vershinin (in type B). We obtain a family of presentations of inverse Artin monoids of type A by cluster mutations.