Ergodic coactions with large multiplicity and monoidal equivalence of quantum groups

源自遍历共作用的量子超群

Quantum hypergroups arising from ergodic coactions

本文研究了通过遍历可积作用得到的量子超群，揭示了其自然共作用结构，并通过等变对应理论刻画了这些超群的共可除性。

紧群在$M_n$上的余作用

Coactions of compact groups on $M_n$

该研究探讨紧群在矩阵代数$M_n$上的余作用性质，证明其与Fell丛的关联及酉实现条件，给出内余作用的等价刻画，明确$\text{SO}(3)$与$\text{SU}(2)$上有效遍历余作用的存在性差异，并提供两类最小有限非阿贝尔群的相关实例。

C*-代数的极大量子群扭张量积

The maximal quantum group-twisted tensor product of C*-algebras

该研究构造了C*-代数极小子量子群扭张量积的极大对应物，证明其满足辫子对易表示泛性，可给出拟三角C*-量子群余作用的幺半结构，是Yetter-Drinfeld C*-代数双范畴的水平合成，且群余作用下与非扭张量积的Rieffel形变一致。

Ergodic actions of the compact quantum group $O_{-1}(2)$

Among the ergodic actions of a compact quantum group $\mathbb{G}$ on possibly non-commutative spaces, those that are {\it embeddable} are the natural analogues of actions of a compact group on its homogeneous spaces. These can be realized as {\it coideal subalgebras} of the function algebra $\mathcal{O}(\mathbb{G})$ attached to the compact quantum group. We classify the embeddable ergodic actions of the compact quantum group $O_{-1}(2)$, basing our analysis on the bijective correspondence between all ergodic actions of the classical group $O(2)$ and those of its quantum twist resulting from th…

Galois objects and cocycle twisting for locally compact quantum groups

In this article, we investigate the notion of a Galois object for a locally compact quantum group M. Such an object consists of a von Neumann algebra N equipped with an ergodic integrable coaction of M on N, such that the crossed product is a type I factor. We show how to construct from such a coaction a new locally compact quantum group P, which we call the reflection of M along N. By way of application, we prove the following statement: any twisting of a locally compact quantum group by a unitary 2-cocycle is again a locally compact quantum group.

C*-代数的量子群扭张量积 II

Quantum group-twisted tensor products of C*-algebras II

本研究针对拟三角C*-量子群，将此前构造的扭张量积强化为C*-代数连续余作用范畴的幺半结构，定义了辫子C*-量子群，并证明紧辫子C*-量子群可通过半直积得到紧量子群。