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Quantum permutation groups: a survey

Teodor Banica·Julien Bichon·Benoit Collins
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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.

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Teodor Banica, Julien Bichon, Benoit Collins. 2007-04-25. Quantum permutation groups: a survey. https://arxiv.org/abs/math/0612724

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