论文标题
抗富含二重的双子
Pre-anti-flexible bialgebra
论文作者
论文摘要
在本文中，我们根据零重量的rota-baxter算子的术语来得出抗富含代数的旋转式操作员的术语，将抗固定前的代数视为抗芬利语的代数拆分代数，并在抗芬兰代数中划分，在抗抗反态的双静脉外静脉和匹配的匹配型和匹配的匹配和配对的匹配和匹配的匹配性群体中，抗富含代数的前代数和前抗双重双重性。对特殊类别的抗饱和双重毛虫的调查导致建立前抗柔性的杨巴克斯特方程。抗抗柔性的代数和树突状代数的双重模块具有相同的形状，并且这种形状都诱导了前抗柔性的Yang-baxter方程和$ \ MATHCAL {D} $ - 方程都是相同的。抗柔性前的杨 - 巴克斯特方程的对称溶液给出了抗抗柔性的双重词。最后，我们回想起并链接$ \ MATHCAL {O} $ - 反芬太语代数的运算符与抗抗柔性代数的双模型，并建立了抗flixible Yang-Baxter方程的对称解决方案。
In this paper, we derive pre-anti-flexible algebras structures in term of zero weight's Rota-Baxter operators defined on anti-flexible algebras, view pre-anti-flexible algebras as a splitting of anti-flexible algebras, introduce the notion of pre-anti-flexible bialgebras and establish equivalences among matched pair of anti-flexible algebras, matched pair of pre-anti-flexible algebras and pre-anti-flexible bialgebras. Investigation on special class of pre-anti-flexible bialgebras leads to the establishment of the pre-anti-flexible Yang-Baxter equation. Both dual bimodules of pre-anti-flexible algebras and dendriform algebras have the same shape and this induces that both pre-anti-flexible Yang-Baxter equation and $\mathcal{D}$-equation are identical. Symmetric solution of pre-anti-flexible Yang-Baxter equation gives a pre-anti-flexible bialgebra. Finally, we recall and link $\mathcal{O}$-operators of anti-flexible algebras to bimodules of pre-anti-flexible algebras and built symmetric solutions of anti-flexible Yang-Baxter equation.
