图C* 代数的量子对称性
Quantum Symmetries of Graph C*-Algebras
摘要：
图C* 代数的研究在算子代数中有着悠久的历史。令人惊讶的是，迄今为止，它们的量子对称性从未被计算过。我们关闭这个差距，证明了量子自同构群的有限，有向图没有重边最大的作用在相应的图C* 代数。这表明图的量子对称性与图C* 代数的量子对称性是一致的。在我们的结果中，我们使用Banica在2005年给出的图的量子自同构群的定义。请注意，Bichon在2003年给出了一个不同的定义;我们的行动受到他的工作的启发。我们回顾和比较这两个定义，我们给出了一个完整的表的量子自同构群（相对于任何两个定义）的无向图的四个顶点。
英文摘要：
The study of graph C*-algebras has a long history in operator algebras. Surprisingly, their quantum symmetries have never been computed so far. We close this gap by proving that the quantum automorphism group of a finite, directed graph without multiple edges acts maximally on the corresponding graph C*-algebra. This shows that the quantum symmetry of a graph coincides with the quantum symmetry of the graph C*-algebra. In our result, we use the definition of quantum automorphism groups of graphs as given by Banica in 2005. Note that Bichon gave a different definition in 2003; our action is inspired from his work. We review and compare these two definitions and we give a complete table of quantum automorphism groups (with respect to either of the two definitions) for undirected graphs on four vertices.
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