论文标题
epivariant $ \ mathrm {c}^*$ - pimsner代数上的Quantum组动作
Equivariant $\mathrm{C}^*$-correspondences and compact quantum group actions on Pimsner algebras
论文作者
论文摘要
令$ g $为紧凑型量子组。我们表明，给定给定$ g $ - equivariant $ \ mathrm {c}^*$ - 通信$ e $，pimsner algebra $ \ mathcal {o} _e $可以自然地制成$ g $ - $ \ $ \ $ \ m mathrm {c}^*$ - algebra。我们还提供了足够的条件，可以保证，Pimsner代数$ \ Mathcal {O} _e $上的$ G $ ACTION以这种方式出现。当$ g $是KAC类型时，$ \ mathrm {kmms} $状态是由pimsner代数的状态，源于准无数量的动态，仅当在将其限制为$ g $ equivariant的天然条件下，且仅当将其限制为$ g $ g $ equivariant而获得的奇特状态时。我们将这些结果应用于$ \ mathrm {c}^*$ - 从有限的，有向图获得的对应关系，并从Banica和Bichon的意义上就此类图的量子自动形态组得出各种结论。
Let $G$ be a compact quantum group. We show that given a $G$-equivariant $\mathrm{C}^*$-correspondence $E$, the Pimsner algebra $\mathcal{O}_E$ can be naturally made into a $G$-$\mathrm{C}^*$-algebra. We also provide sufficient conditions under which it is guaranteed that a $G$-action on the Pimsner algebra $\mathcal{O}_E$ arises in this way, in a suitable precise sense. When $G$ is of Kac type, a $\mathrm{KMS}$ state on the Pimsner algebra, arising from a quasi-free dynamics, is $G$-equivariant if and only if the tracial state obtained from restricting it to the coefficient algebra is $G$-equivariant, under a natural condition. We apply these results to the situation when the $\mathrm{C}^*$-correspondence is obtained from a finite, directed graph and draw various conclusions on the quantum automorphism groups of such graphs, both in the sense of Banica and Bichon.
