no. 3
Quantum automorphisms of folded cube graphs
[Automorphismes quantiques des graphes des cubes pliés]
Schmidt, Simon1
1 Saarland University, Fachbereich Mathematik 66041 Saarbrücken (Germany)
Annales de l'Institut Fourier, Tome 70 (2020) no. 3, pp. 949-970.

On démontre que le groupe quantique d’automorphismes du graphe de Clebsch est SO 5 -1 ce qui répond à une question de Banica, Bichon et Collins de 2007. En général, pour des valeurs impaires de n, le groupe quantique d’automorphisme du graphe du n-cube plié est SO n -1 . En plus, on démontre qu’un graphe possède des symétries quantiques, si son groupe d’automorphismes contient une paire d’automorphismes disjoints.

We show that the quantum automorphism group of the Clebsch graph is SO 5 -1 . This answers a question by Banica, Bichon and Collins from 2007. More general for odd n, the quantum automorphism group of the folded n-cube graph is SO n -1 . Furthermore, we show that if the automorphism group of a graph contains a pair of disjoint automorphisms this graph has quantum symmetry.

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DOI : 10.5802/aif.3328
Classification : 46LXX, 20B25, 05CXX
Keywords: finite graphs, graph automorphisms, automorphism groups, quantum automorphisms, quantum groups, quantum symmetries
Mot clés : graphes finis, automorphismes des graphes, groupes d’automorphismes, automorphismes quantiques, groupes quantiques, symétries quantiques

Schmidt, Simon 1

1 Saarland University, Fachbereich Mathematik 66041 Saarbrücken (Germany)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Schmidt, Simon. Quantum automorphisms of folded cube graphs. Annales de l'Institut Fourier, Tome 70 (2020) no. 3, pp. 949-970. doi : 10.5802/aif.3328. https://aif.centre-mersenne.org/articles/10.5802/aif.3328/

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