Trivialisations dans les catégories tannakiennes
Half-liberated real spheres and their subspaces
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
We consider circulant graphs having vertices, with prime. To any such graph we associate a certain number , that we call type of the graph. We prove that for 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
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...
Cosemisimple Hopf algebras with antipode of arbitrary finite order.
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