论文标题
（偏斜）牙套的杨巴克斯特方程的新型非接收溶液
Novel non-involutive solutions of the Yang-Baxter equation from (skew) braces
论文作者
论文摘要
我们产生了来自（偏斜）括号的杨巴克斯特方程的新型非进度溶液。这些解决方案是对来自牙套和偏斜牙套的已知方法的概括，而且在牙套的情况下，它们不一定是涉及的。如果是双面（偏斜）括号，则可以将此类解决方案分配给集合的每个元素。还引入了与逆溶液相关的新型徒图。此外，我们表明，最近派生的涉及案例的德林菲尔德曲折仍然可以在非涉及的框架中接受，并且我们确定了扭曲的$ r $ $ $ $ $ $ $ $ $ $ $ $ $ $ $。我们观察到，在参与案例中，正如人们所期望的那样，潜在的量子代数不是准三角形的双gebra，而是准三角形的准二极管。与涉及案例相反的扭曲$ r $ - amatrices的量子代数也是如此。
We produce novel non-involutive solutions of the Yang-Baxter equation coming from (skew) braces. These solutions are generalisations of the known ones coming from braces and skew braces, and surprisingly in the case of braces they are not necessarily involutive. In the case of two-sided (skew) braces one can assign such solutions to every element of the set. Novel bijective maps associated to the inverse solutions are also introduced. Moreover, we show that the recently derived Drinfeld twists of the involutive case are still admissible in the non-involutive frame and we identify the twisted $r$-matrices and twisted coproducts. We observe, as in the involutive case that the underlying quantum algebra is not a quasi-triangular bialgebra, as one would expect, but a quasi-triangular quasi-bialgebra. The same applies to the quantum algebra of the twisted $r$-matrices, contrary to the involutive case.
