论文标题
逆半束和杨巴克斯特方程
Inverse semi-braces and the Yang-Baxter equation
论文作者
论文摘要
本文的主要目的是在这些新的志愿者中提供不一定具有肉类的杨巴克斯特方程的设定理论解决方案。在具体的情况下，我们借鉴了逆半群的经典理论以及最近研究的牙套的经典理论，以对寻找解决方案的开放问题给出新的研究观点。也就是说，我们可以求助于一种新的结构，即逆半手架，这是一个三重$（s， +，\ cdot）$，带有$（s， +）$ a semigroup和$（s，\ cdot）$（s，\ cdot）$ anderveSemigroup满足关系$ a \ a \ a \ a \ left（b + c \ right）= b + c \ right） $ a，b，c \ in s $，其中$ a^{ - 1} $是$ a $ in $（s，\ cdot）$的倒数。特别是，我们给出了几个反向半构图的结构，这些结构允许获得与已知直至的解决方案不同的解决方案。
The main aim of this paper is to provide set-theoretical solutions of the Yang-Baxter equation that are not necessarily bijective, among these new idempotent ones. In the specific, we draw on both to the classical theory of inverse semigroups and to that of the most recently studied braces, to give a new research perspective to the open problem of finding solutions. Namely, we have recourse to a new structure, the inverse semi-brace, that is a triple $(S,+, \cdot)$ with $(S,+)$ a semigroup and $(S, \cdot)$ an inverse semigroup satisfying the relation $a \left(b + c\right) = a b + a\left(a^{-1} + c\right)$, for all $a,b,c \in S$, where $a^{-1}$ is the inverse of $a$ in $(S, \cdot)$. In particular, we give several constructions of inverse semi-braces which allow for obtaining solutions that are different from those until known.
