On the uniqueness of AF diagonals in regular limit algebras

Pseudo-Diagonals and Uniqueness Theorems

We examine a certain type of abelian C*-subalgebras that allow one to give a unified treatment of two uniqueness theorems: for graph C*-algebras and for certain reduced crossed products.

源于广义对角连接映射的 AH-代数中的 C$^*$-对角：谱与唯一性

C$^*$-diagonals in AH-algebras arising from generalized diagonal connecting maps: spectrum and uniqueness

本文将 Bratteli 型图关联到源于广义对角连接映射的 AH-代数，通过引入谱不完备概念刻画谱连通分量，证明了部分 AI-代数不具备唯一的归纳极限 Cartan 子代数，并探讨了 AF-代数的唯一性。

广义布尔动力系统的广义唯一性定理

A generalized uniqueness theorem for generalized Boolean dynamical systems

本研究刻画广义布尔动力系统相关C*-代数的典范对角子代数，引入阿贝尔核这一交换子代数，并在B、L可数的假设下建立C*-代数*-同态单射性等价于其在阿贝尔核上限制单射的唯一性定理。

Uniqueness of trace and C*-simplicity beyond regular representation

A discrete group $Γ$ is C*-simple if the C*-algebra $C_λ^*(Γ)$ generated by the range of the left regular representation $λ$ on $\ell^2(Γ)$ is simple. In this case, $Γ$ acts faithfully on the Furstenberg boundary $\partial_FΓ$ and there is a unique trace on $C_λ^*(Γ)$. In this paper we study the unique trace property for the C*-algebra $C_π^*(Γ)$ generated by the range of an arbitrary unitary representation $π: Γ\to B(H_π) $ and relate it to the faithfulness of the action of $Γ$ on the Furstenberg-Hamana boundary $\mathcal B_π$. Similar relation is obtained between simplicity of $C_π^*(Γ)$ and…

正则对角子因子

Regular diagonal subfactors

研究来自\(II_1\)型因子\(Q\)自同构族的对角子因子正则性，证明其正则性与自同构类基数、子群等有关，且正则性图景是图论的，还给出了对角子因子深度准则，有助于刻画正则性。