Right $\ell$-groups associated with von Neumann algebras

从von Neumann algebras的深度二包含到量子群胚的有限群的相对匹配对

Relative matched pairs of finite groups from depth two inclusions of von Neumann algebras to quantum groupoids

在这项工作中，我们给出了一个推广的匹配对（有限）群来描述一般类的深度2包含的因子冯诺依曼代数和C*-量子群胚与，使用双群胚。

Quantum smooth uncertainty principles for von Neumann bi-algebras

In this article, we prove various smooth uncertainty principles on von Neumann bi-algebras, which unify numbers of uncertainty principles on quantum symmetries, such as subfactors, and fusion bi-algebras etc, studied in quantum Fourier analysis. We also obtain Widgerson-Wigderson type uncertainty principles for von Neumann bi-algebras. Moreover, we give a complete answer to a conjecture proposed by A. Wigderson and Y. Wigderson.

具有vonNeumann正则Cartan生成元的量子包络代数及Pierce分解

Quantum enveloping algebras with von Neumann regular Cartan-like generators and the Pierce decomposition

引入并研究了由Uq（sl 2）导出的包含幂等元和vonNeumann正则Cartan生成元的量子双代数。在这些双代数上构造了各种类型的对极（可逆的和vonNeumann正则的），分别得到了一个霍普夫代数结构和一个vonNeumann-霍普夫代数结构.对于它们，给出了一些特殊的R-矩阵（可逆矩阵和von Neumann正则矩阵）的显式形式，后者考虑了Pierce分解。