论文标题
Clifford Semigroups和Yang-Baxter方程式的Rota-Baxter操作员
Rota-Baxter operators on Clifford semigroups and the Yang-Baxter equation
论文作者
论文摘要
In this paper, we introduce the theory of Rota-Baxter operators on Clifford semigroups, useful tools for obtaining dual weak braces, i.e., triples $\left(S,+,\circ\right)$ where $\left(S,+\right)$ and $\left(S,\circ\right)$ are Clifford semigroups such that $a\circ\left(b+c\right) = A \ Circ B -a +a \ circ c $和$ a \ circ a^ - = -a +a $，对于所有$ a，b，c \ in S $。对于每个代数结构，Yang-Baxter方程的固定理论解相关，该方程的行为接近了徒行为和非分类。从克利福德半群的理论中，我们提供了构建双重弱牙套并加深某些结构方面的方法，包括理想的概念。
In this paper, we introduce the theory of Rota-Baxter operators on Clifford semigroups, useful tools for obtaining dual weak braces, i.e., triples $\left(S,+,\circ\right)$ where $\left(S,+\right)$ and $\left(S,\circ\right)$ are Clifford semigroups such that $a\circ\left(b+c\right) = a\circ b - a +a\circ c$ and $a\circ a^- = -a+a$, for all $a,b,c\in S$. To each algebraic structure is associated a set-theoretic solution of the Yang-Baxter equation that has a behaviour near to the bijectivity and non-degeneracy. Drawing from the theory of Clifford semigroups, we provide methods for constructing dual weak braces and deepen some structural aspects, including the notion of ideal.
