The boundary of universal discrete quantum groups, exactness and factoriality

Exactness of universal free products of finite dimensional $C^*$-algebras with amalgamation

We investigate free products of finite dimensional $C^*$-algebras with amalgamation over diagonal subalgebras. We look to determine under what circumstances a given free product is exact and/or nuclear. In some cases we find a description of the algebra in terms of a more readily understood algebra.

On nuclearity and exactness of the tame C*-algebras associated with finitely separated graphs

We introduce a graph theoretic property called Condition (N) for finitely separated graphs and prove that it is equivalent to both nuclearity and exactness of the associated universal tame graph C*-algebra.

弱正合性与冯·诺依曼代数的融合自由积

Weak exactness and amalgamated free product of von Neumann algebras

本文证明弱正合冯·诺依曼代数的融合自由积仍弱正合，方法利用Toeplitz-Pimsner代数的泛性质及双模上的局部凸拓扑刻画弱正合性。

A relationship between HNN extensions and amalgamated free products in operator algebras

With a minor change made in the previous construction we observe that any reduced HNN extension is precisely a compressed algebra of a certain reduced amalgamated free product in both the von Neumann algebra and the $C^*$-algebra settings. It is also pointed out that the same fact holds true even for universal HNN extensions of C$^*$-algebras. We apply the observation to the questions of factoriality and type classification of HNN extensions of von Neumann algebras and also those of simplicity and $K$-theory of (reduced or universal) HNN extensions of $C^*$-algebras.

泛量子同态的算子代数

Operator Algebras of Universal Quantum Homomorphisms

本文研究两个幺正C*-代数A和B生成的泛幺正C*-代数$\u2102(A,B)$的存在性及性质，分析有限维B时的LP、RFD等性质，构造约化版本并研究其特征，证明无限维B时$\u2102(A,B)$仅在B有限维时存在，还探讨了量子半群结构。

源于图积的泛 C$^{\ast}$-代数：结构与应用

Universal C$^{\ast}$-Algebras from Graph Products: Structure and Applications

本文引入并研究了一类由 C$^{\ast}$-代数的 reduced graph products 生成并辅以投影族扩充的泛 C$^{\ast}$-代数，利用其组合结构确立了泛性质、核性、精确性与理想结构，并借此为图积 C$^{\ast}$-代数结构提供了新见解。