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Models of quantum permutations
Journal of Functional Analysis ( IF 1.7 ) Pub Date : 2020-08-01 , DOI: 10.1016/j.jfa.2020.108516
Stefan Jung , Moritz Weber

For $N\ge 4$ we present a series of *-homomorphisms $\varphi_n:C(S_N^+)\rightarrow B_n$ where $S_N^+$ is the quantum permutation group. They are not necessarily representations of the quantum group $S_N^+$ but they yield good operator algebraic models of quantum permutation matrices. The C*-algebras $B_n$ allow the construction of an inverse limit $B_{\infty}$ which defines a compact matrix quantum group $S_N\subsetneq G\subseteq S_N^+$. We know $G=S_N^+$ for $N=4,5$ from Banica's work, but we have to leave open the case $N\ge 6$.

中文翻译:

量子排列模型

对于 $N\ge 4$ 我们提出了一系列 *-同态 $\varphi_n:C(S_N^+)\rightarrow B_n$ 其中 $S_N^+$ 是量子置换群。它们不一定是量子群 $S_N^+$ 的表示,但它们产生了量子置换矩阵的良好算子代数模型。C*-代数 $B_n$ 允许构造一个逆极限 $B_{\infty}$,它定义了一个紧致矩阵量子群 $S_N\subsetneq G\subseteq S_N^+$。我们从 Banica 的工作中知道 $G=S_N^+$ 为 $N=4,5$,但我们必须保持打开案例 $N\ge 6$。
更新日期:2020-08-01
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