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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-1,
author = {Teodor Banica and Julien Bichon and Beno\^\i t Collins},
title = {Quantum permutation groups: a survey},
journal = {Banach Center Publications},
volume = {75},
year = {2007},
pages = {13-34},
zbl = {1140.46329},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-1}
}
Teodor Banica; Julien Bichon; Benoît Collins. Quantum permutation groups: a survey. Banach Center Publications, Tome 75 (2007) pp. 13-34. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-1/