On the classification of Galois objects over the quantum group of a nondegenerate bilinear form

Center and Universal R-matrix for Quantized Borcherds Superalgebras

We construct a nondegenerate symmetric bilinear form on quantized enveloping algebras associated to Borcherds superalgebras. With this, we study its center and its universal R-matrix.

超势代数的量子对称等价

Quantum-symmetric equivalence for superpotential algebras

本文引入量子对称等价概念，利用双伽罗瓦对象刻画超势代数的正则性与数值不变量。

Graded twisting of categories and quantum groups by group actions

Given a Hopf algebra $A$ graded by a discrete group together with an action of the same group preserving the grading, we define a new Hopf algebra, which we call the graded twisting of $A$. If the action is adjoint, this new Hopf algebra is a twist of $A$ by a pseudo-$2$-cocycle. Analogous construction can be carried out for monoidal categories. As examples we consider graded twistings of the Hopf algebras of nondegenerate bilinear forms, their free products, hyperoctahedral quantum groups and $q$-deformations of compact semisimple Lie groups. As applications, we show that the analogues of the…

自由酉量子群与泛共主权Hopf代数的自由分解

Free resolutions for free unitary quantum groups and universal cosovereign Hopf algebras

本研究构造了自由酉量子群与一般参数矩阵下泛共主权Hopf代数余单位的有限自由分解，结合Yetter-Drinfeld结构与相关理论计算了其上同调，并推广了粘合自由积与投射分解的适用范围。