A New Approach to Braided T-Categories and Generalized Quantum Yang–Baxter Equations

We introduce and study a large class of coalgebras (possibly (non)coassociative) with group-algebraic structures Hopf (non)coassociative group-algebras. Hopf (non)coassociative group-algebras provide a unifying framework for classical Hopf algebras and Hopf group-algebras and Hopf coquasigroups. We introduce and discuss the notion of a quasitriangular Hopf (non)coassociative π-algebra and show some of its prominent properties, e.g., antipode S is bijective. As an application of our theory, we construct a new braided T-category and give a new solution to the generalized quantum Yang–Baxter equation.

我们引入并研究了一大类具有群代数结构的余代数（可能是（非）余结合的），即霍普夫（非）余结合群代数。霍普夫（非）余结合群代数为经典霍普夫代数、霍普夫群代数以及霍普夫余拟群提供了一个统一的框架。我们引入并讨论了拟三角霍普夫（非）余结合π - 代数的概念，并展示了它的一些显著性质，例如，对极S是双射的。作为我们理论的一个应用，我们构造了一个新的辫子T - 范畴，并给出了广义量子杨 - 巴克斯特方程的一个新解。