A few remarks on mixing properties of $C^*$-dynamical systems

关于C*代数包含关系中中间子代数的一些评论

A few remarks on intermediate subalgebras of an inclusion of C*-algebras

本文研究了简单C*代数包含关系中中间子代数的角度稳定性，并改进了中间子代数 lattice 的基数上界。

A few remarks on exact C(X)-algebras

We extend in this paper several results of E. Kirchberg, S. Wassermann and the author dealing with continuous fields of C*--algebras to the semi-continuous case. We provide a new characterisation of separable lower semi-continuity C*--bundles and we present exactness criteria for C(X)-algebras and unital bisimplifiable Hopf \cst-algebras.

关于Pimsner-Popa基和深度为2的正则子因子的几点注记

A few remarks on Pimsner-Popa bases and regular subfactors of depth 2

本文研究了深度为2的正则子因子的性质，证明了其具有双侧Pimsner-Popa基，并探讨了交叉积子因子的结构。

A few remarks on the tube algebra of a monoidal category

We prove two results on the tube algebras of rigid C$^*$-tensor categories. The first is that the tube algebra of the representation category of a compact quantum group $G$ is a full corner of the Drinfeld double of $G$. As an application we obtain some information on the structure of the tube algebras of the Temperley-Lieb categories $TL(d)$ for $d>2$. The second result is that the tube algebras of weakly Morita equivalent C$^*$-tensor categories are strongly Morita equivalent. The corresponding linking algebra is described as the tube algebra of the $2$-category defining the Morita context.