On Structure Groups of Set-Theoretic Solutions to the Yang–Baxter Equation
نویسندگان
چکیده
منابع مشابه
Coxeter-like Groups for Groups of Set-theoretic Solutions of the Yang–baxter Equation
We attach with every finite, involutive, nondegenerate set-theoretic solution of the Yang–Baxter equation a finite group that plays for the associated structure group the role that a finite Coxeter group plays for the associated Artin–Tits group.
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نشان می دهیم که هر اشتقاق لی روی یک c^*-جبر به شکل استاندارد است، یعنی می تواند به طور یکتا به مجموع یک اشتقاق لی و یک اثر مرکز مقدار تجزیه شود. کلمات کلیدی: اشتقاق، اشتقاق لی، c^*-جبر.
15 صفحه اولRetractability of Set Theoretic Solutions of the Yang-baxter Equation *
It is shown that square free set theoretic involutive non-degenerate solutions of the Yang-Baxter equation whose associated permutation group (referred to as an involutive Yang-Baxter group) is abelian are retractable in the sense of Etingof, Schedler and Soloviev. This solves a problem of Gateva-Ivanova in the case of abelian IYB groups. It also implies that the corresponding finitely presente...
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A Combinatorial Approach to the Set-theoretic Solutions of the Yang-baxter Equation
A bijective map r : X −→ X, where X = {x1, · · · , xn} is a finite set, is called a set-theoretic solution of the Yang-Baxter equation (YBE) if the braid relation r12r23r12 = r23r12r23 holds in X. A non-degenerate involutive solution (X, r) satisfying r(xx) = xx, for all x ∈ X, is called squarefree solution. There exist close relations between the square-free set-theoretic solutions of YBE, the...
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 2019
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091518000548