论文标题
抗刺激性双重毛虫
Anti-flexible bialgebras
论文作者
论文摘要
在本文中，我们建立了一种抗芬太语代数的双重理论。我们介绍了抗柔滑的双gge骨的概念，该抗曲子等同于抗抗抑郁的代数的三重。对抗弹性双重双ge的特殊情况的研究导致在反芬太语的代数中引入反弹性的杨巴克斯特方程，该代数是在lie代数或联想Algebra中的lie代数或联想的Yang-baxter方程中的经典杨手机方程的类似物。抗柔性的杨巴克斯特方程和关联杨 - 巴克斯特方程都具有相同的形式，这是一个出乎意料的结果。抗柔性的杨巴克斯特方程的偏斜对称溶液可产生抗曲折的双齿bra。最后，引入了抗曲折的代数和前芬特式代数的$ \数学o $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $的操作员，以构建反芬太语阳报方程的偏斜 - 对称解决方案。
We establish a bialgebra theory for anti-flexible algebras in this paper. We introduce the notion of an anti-flexible bialgebra which is equivalent to a Manin triple of anti-flexible algebras. The study of a special case of anti-flexible bialgebras leads to the introduction of anti-flexible Yang-Baxter equation in an anti-flexible algebra which is an analogue of the classical Yang-Baxter equation in a Lie algebra or the associative Yang-Baxter equation in an associative algebra. It is a unexpected consequence that both the anti-flexible Yang-Baxter equation and the associative Yang-Baxter equation have the same form. A skew-symmetric solution of anti-flexible Yang-Baxter equation gives an anti-flexible bialgebra. Finally the notions of an $\mathcal O$-operator of an anti-flexible algebra and a pre-anti-flexible algebra are introduced to construct skew-symmetric solutions of anti-flexible Yang-Baxter equation.
