We define a notion of quantum automorphism groups of graph [Formula: see text]-algebras for finite, connected graphs. Under the assumption that the underlying graph does not have any multiple edge or loop, the quantum automorphism group of the underlying directed graph in the sense of Banica [Quantum automorphism groups of homogeneous graphs, J. Funct. Anal. 224 (2005) 243–280] (which is also the symmetry object in the sense of [S. Schmidt and M. Weber, Quantum symmetry of graph [Formula: see text]-algebras, arXiv:1706.08833 ] is shown to be a quantum subgroup of quantum automorphism group in our sense. Quantum symmetries for some concrete graph [Formula: see text]-algebras have been computed.

中文翻译：

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与连通图相关的图 C*-代数的量子对称性

我们定义了图的量子自同构群的概念[公式：见正文]-用于有限连通图的代数。在基础图不具有任何多重边或环的假设下，Banica 意义上的基础有向图的量子自同构群 [Quantum automorphism groups of homogeneous graph, J. Funct. 肛门。224 (2005) 243–280]（这也是 [S. Schmidt 和 M. Weber, Quantum Symmetry of graph [Formula: see text]-algebras, arXiv:1706.08833 ] 意义上的对称对象我们意义上的量子自同构群的量子子群。已经计算了一些具体图[公式：见文本]-代数的量子对称性。