论文标题
有限空间的任何量子对称性
Anyonic quantum symmetries of finite spaces
论文作者
论文摘要
我们构建了量子置换群组的编织类似物，并表明它是$ \ Mathbb {z}/n \ Mathbb {z} $ - $ \ $ \ textrm {c}^*$ algebras具有带有扭曲的单域结构的通用编织的紧凑型量子组。作为一种应用，我们证明存在有限，简单，无向，循环图的编织量子对称性，并明确计算了几个示例，并在此方向上获得了BANICA结果的概括。最后，在附录中，我们简要描述了量子置换组及其融合规则的编织类似物的不可约说明。
We construct a braided analogue of the quantum permutation group and show that it is the universal braided compact quantum group acting on a finite space in the category of $\mathbb{Z}/N\mathbb{Z}$-$\textrm{C}^*$-algebras with a twisted monoidal structure. As an application, we prove the existence of braided quantum symmetries of finite, simple, undirected, circulant graphs, explicitly compute it for several examples, and obtain a generalization of a result of Banica in this direction. Finally, in an appendix, we briefly describe the irreducible representations of this braided analogue of the quantum permutation group and their fusion rules.
