Quantum permutation groups: a survey

By T. Banica, Julien Bichon, Benoît Collins. 2006

76 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/be023ec8e7b42be4f0e215d513d069105261396b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Roland Speicher
2. Stephen J. Curran
3. T. Banica
4. Julien Bichon
5. Michael Brannan
6. Benoît Collins

In Geometry and Topology

1. Roland Speicher
2. Stephen J. Curran
3. T. Banica
4. Moritz Weber
5. Sven Raum
6. Michael Brannan
7. Julien Bichon
8. Amaury Freslon

In Mathematical Physics

1. Roland Speicher
2. Stephen J. Curran
3. T. Banica
4. Moritz Weber
5. Sven Raum
6. Michael Brannan
7. Julien Bichon
8. Benoît Collins

Citations in the corpus

• Liberation of orthogonal Lie groups (2008, background): “Most results here were obtained in the last few years, and we refer to [5] for a survey.”
• Algebraic quantum permutation groups (2007, unknown): “We refer the 2000 Mathematics Subject Classification.”
• Classification results for easy quantum groups (2009, background): “However, a ray of light comes from a conjecture in [5], stating that there is no intermediate quantum group Sn ⊂ G ⊂ S n .”