Quantum permutation groups: a survey

Details Quantum permutation groups: a survey Quantum permutation groups: a survey

2006-12-22

arxiv.org/abs/math/0612724v2

Banach Center Publ. 78 (2007), 13-34

Mathematics

Combinatorics

19 pages

Scientific paper

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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