Quantum permutation groups: a survey
Volume 78 / 2007
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.
