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arXiv · 1706.08833

Quantum Symmetries of Graph C*-Algebras

Simon Schmidt·Moritz Weber
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Abstract

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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Simon Schmidt, Moritz Weber. 2017-06-27. Quantum Symmetries of Graph C*-Algebras. https://doi.org/10.4153/cmb-2017-075-4

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