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Free Wreath Product by the Quantum Permutation Group

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Abstract

Let A be a compact quantum group, let n∈N * and let A aut(X n ) be the quantum permutation group on n letters. A free wreath product construction A*w A aut(X n ) is introduced. This construction provides new examples of quantum groups, and is useful to describe the quantum automorphism group of the n-times disjoint union of a finite connected graph.

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References

  1. Avitzour, D.: Free products of C*-algebras, Trans. Amer. Math. Soc. 271(2) (1982), 423-435.

    Google Scholar 

  2. Banica, T.: Symmetries of a generic coaction, Math. Ann. 314 (1999), 763-780.

    Google Scholar 

  3. Bichon, J.: Quantum automorphism groups of finite graphs, Proc. Amer. Math. Soc. 131(3) (2003), 665-673.

    Google Scholar 

  4. Bichon, J.: Galois reconstruction of finite quantum groups, J. Algebra 230 (2000), 683-693.

    Google Scholar 

  5. Hewitt, E. and Ross, K. A.: Abstract Harmonic Analysis, Vol. 2, Springer, New York, 1969.

    Google Scholar 

  6. Iltis, R.: Some algebraic structure on the dual of a compact group, Canad. J. Math. 20 (1968), 1499-1510.

    Google Scholar 

  7. Klimyk, A. and Schmüdgen, K.: Quantum Groups and their Representations, Texts Monogr. Phys., Springer, New York, 1997.

    Google Scholar 

  8. Van Daele, A. and Wang, S.: Universal quantum groups, Internat. J. Math. 7 (1996), 255-263.

    Google Scholar 

  9. Voiculescu, D.: Symmetries of some reduced free product C*-algebras, In: Operator Algebras and their Connections with Topology and Ergodic Theory, Lecture Notes in Math. 1132, Springer, New York, 1985, pp. 556-588.

    Google Scholar 

  10. Wang, S.: Free products of compact quantum groups, Comm. Math. Phys. 167 (1995), 671-692.

    Google Scholar 

  11. Wang, S.: Quantum symmetry groups of finite spaces, Comm. Math. Phys. 195 (1998), 195-211.

    Google Scholar 

  12. Woronowicz, S. L.: Twisted SU(2) group. An example of noncommutative differential calculus, Publ. RIMS Kyoto 23 (1987), 117-181.

    Google Scholar 

  13. Woronowicz, S. L.: Compact matrix pseudogroups, Comm. Math. Phys. 111 (1987), 613-665.

    Google Scholar 

  14. Woronowicz, S. L.: Tannaka-Krein duality for compact matrix pseudogroups. Twisted SU(N) groups, Invent. Math. 93 (1988), 35-76.

    Google Scholar 

  15. Woronowicz, S. L.: A remark on compact matrix quantum groups, Lett. Math. Phys. 21 (1991), 35-39.

    Google Scholar 

  16. Woronowicz, S. L.: Compact quantum groups, In: 'Symétries quantiques' (Les Houches, 1995), North-Holland, Amsterdam, 1998, pp. 845-884.

    Google Scholar 

Download references

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  1. Laboratoire de Mathématiques Appliquées, Université de Pau et des Pays de l'Adour, IPRA, Avenue de l'université, 64000, Pau, France. e-mail

    Julien Bichon

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  1. Julien Bichon
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Bichon, J. Free Wreath Product by the Quantum Permutation Group. Algebras and Representation Theory 7, 343–362 (2004). https://doi.org/10.1023/B:ALGE.0000042148.97035.ca

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