A+ CATEGORY SCIENTIFIC UNIT

Quantum permutation groups: a survey

Volume 78 / 2007

Teodor Banica, Julien Bichon, Benoît Collins Banach Center Publications 78 (2007), 13-34 MSC: Primary 46L65; Secondary 46L37, 46L54, 46L87. DOI: 10.4064/bc78-0-1

Abstract

This is a presentation of recent work on quantum permutation groups. Contains: a short introduction to operator algebras and Hopf algebras; quantum permutation groups, and their basic properties; diagrams, integration formulae, asymptotic laws, matrix models; the hyperoctahedral quantum group, free wreath products, quantum automorphism groups of finite graphs, graphs having no quantum symmetry; complex Hadamard matrices, cocycle twists of the symmetric group, quantum groups acting on $4$ points; remarks and comments.

Authors

  • Teodor BanicaDepartment of Mathematics
    Paul Sabatier University
    118 route de Narbonne
    31062 Toulouse, France
    e-mail
  • Julien BichonDepartment of Mathematics
    Blaise Pascal University
    Campus des Cezeaux
    63177 Aubière Cedex, France
    e-mail
  • Benoît CollinsDepartment of Mathematics
    Claude Bernard University
    43 bd du 11 novembre 1918
    69622 Villeurbanne, France
    e-mail

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