Studies of algebro-geometric aspects on dynamical Yang-Baxter maps

我们构造了与量子动力学Yang-Baxter方程的集合论解--动力学Yang-Baxter映射相关联的双代数胚。每个双代数胚提供了由其动力学表示组成的张量范畴。这个双代数胚是前张量范畴的余代数对象;这样的范畴论性质催生了动力表示的张量范畴。利用主齐性空间构造了动力学Yang-Baxter映射。

We constructed bialgebroids associated with dynamical Yang-Baxter maps, set-theoretic solutions to the quantum dynamical Yang-Baxter equation. Each bialgebroid provides with the tensor category consisting of its dynamical representations. This bialgebroid is a coalgebra object of a pre-tensor category ; and such category-theoretic properties give birth to the tensor category of dynamical representations. We also constructed the dynamical Yang-Baxter map by means of the principal homogeneous space.