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Half-liberated real spheres and their subspaces

Julien Bichon — 2016

Colloquium Mathematicae

We describe the quantum subspaces of Banica-Goswami's half-liberated real spheres, showing in particular that there is a bijection between the symmetric ones and the conjugation stable closed subspaces of the complex projective spaces.

Graphs having no quantum symmetry

Teodor BanicaJulien BichonGaëtan Chenevier — 2007

Annales de l’institut Fourier

We consider circulant graphs having p vertices, with p prime. To any such graph we associate a certain number k , that we call type of the graph. We prove that for p k the graph has no quantum symmetry, in the sense that the quantum automorphism group reduces to the classical automorphism group.

Quantum permutation groups: a survey

Teodor BanicaJulien BichonBenoît Collins — 2007

Banach Center Publications

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...

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