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Quantum automorphism groups of finite graphs


Author: Julien Bichon
Journal: Proc. Amer. Math. Soc. 131 (2003), 665-673
MSC (2000): Primary 16W30, 46L87
DOI: https://doi.org/10.1090/S0002-9939-02-06798-9
Published electronically: October 15, 2002
MathSciNet review: 1937403
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Abstract: A quantum analogue of the automorphism group of a finite graph is introduced. These are quantum subgroups of the quantum permutation groups defined by Wang. The quantum automorphism group is a stronger invariant for finite graphs than the usual automorphism group. We get a quantum dihedral group $D_4$.


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  • 1. T. BANICA, Quantum groups acting on $N$ points, complex Hadamard matrices, and a construction of subfactors, Preprint OA/9806054.
  • 2. T. BANICA, Symmetries of a generic coaction, Math. Ann. 314, 763-780, 1999. MR 2001g:46146
  • 3. A. CONNES, Noncommutative geometry. London: Academic Press, 1994. MR 95j:46063
  • 4. M.S. DIJKHUIZEN, T.H. KOORNWINDER, CQG algebras: a direct algebraic approach to compact quantum groups, Lett. Math. Phys. 32, 315-330, 1994. MR 95m:16029
  • 5. Y. MANIN, Quantum groups and noncommutative geometry. Publications du CRM 1561, Univ. de Montréal, 1988. MR 91e:17001
  • 6. A. VAN DAELE, The Haar measure on a compact quantum group, Proc. Amer. Math. Soc. 123 (10), 3125-3128, 1995. MR 95m:46097
  • 7. S. WANG, Free products of compact quantum groups, Comm. Math. Phys. 167, 671-692, 1995. MR 95k:46104
  • 8. S. WANG, Quantum symmetry groups of finite spaces, Comm. Math. Phys. 195, 195-211, 1998. MR 99h:58014
  • 9. S.L. WORONOWICZ, Compact matrix pseudogroups, Comm. Math. Phys. 111, 613-665, 1987. MR 88m:46079
  • 10. S.L. WORONOWICZ, Tannaka-Krein duality for compact matrix pseudogroups. Twisted $SU(N)$ groups, Invent. Math. 93, 35-76, 1988. MR 90e:22033
  • 11. S.L. WORONOWICZ, Compact quantum groups, in ``Symétries quantiques'' (Les Houches, 1995), North Holland, Amsterdam, 1998, 845-884. MR 99m:46164

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Additional Information

Julien Bichon
Affiliation: Département des Sciences Mathématiques, case 051, Université Montpellier II, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France
Address at time of publication: Département de Mathématiques, Université de Pau et de Pays de l’Adour, Avenue de l’université, 64000 Pau, France
Email: Julien.Bichon@univ-pau.fr

DOI: https://doi.org/10.1090/S0002-9939-02-06798-9
Received by editor(s): December 23, 1998
Received by editor(s) in revised form: March 21, 2000
Published electronically: October 15, 2002
Communicated by: David R. Larson
Article copyright: © Copyright 2002 American Mathematical Society

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