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Dive into the research topics where Julien Bichon is active.

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Featured researches published by Julien Bichon.


Communications in Mathematical Physics | 2006

Ergodic Coactions with Large Multiplicity and Monoidal Equivalence of Quantum Groups

Julien Bichon; An De Rijdt; Stefaan Vaes

We construct new examples of ergodic coactions of compact quantum groups, in which the multiplicity of an irreducible corepresentation can be strictly larger than the dimension of the latter. These examples are obtained using a bijective correspondence between certain ergodic coactions on C*-algebras and unitary fiber functors on the representation category of a compact quantum group. We classify these unitary fiber functors on the universal orthogonal and unitary quantum groups. The associated C*-algebras and von Neumann algebras can be defined by generators and relations, but are not yet well understood.


arXiv: Quantum Algebra | 2003

Quantum automorphism groups of finite graphs

Julien Bichon

A quantum analogue of the automorphism group of a finite graph is introduced. These are quantum subgroups of the quantum permutation groups defined by Wang. The quantum automorphism group is a stronger invariant for finite graphs than the usual automorphism group. We get a quantum dihedral group D 4 .


Communications in Algebra | 2003

The Representation Category of the Quantum Group of a Non-degenerate Bilinear Form

Julien Bichon

Abstract We show that the representation category of the quantum group of a non-degenerate bilinear form is monoidally equivalent to the representation category of the quantum group SL q (2) for a well chosen non-zero parameter q. The key ingredient for the proof of this result is the direct and explicit construction of an appropriate Hopf bigalois extension. Then we get, when the base field is of characteristic zero, a full description of cosemisimple Hopf algebras whose representation semi-ring is isomorphic to the one of SL(2).


Crelle's Journal | 2009

QUANTUM GROUPS ACTING ON 4 POINTS

Teodor Banica; Julien Bichon

Abstract We classify the compact quantum groups acting on 4 points. These are the quantum subgroups of the quantum permutation group 𝓠4. Our main tool is a new presentation for the algebra C(𝓠4), corresponding to an isomorphism of type 𝓠4 ≃ SO –1(3). The quantum subgroups of 𝓠4 are subject to a McKay type correspondence, that we describe at the level of algebraic invariants.


Journal of Pure and Applied Algebra | 2001

Cosovereign Hopf algebras

Julien Bichon

Abstract A sovereign monoidal category is an autonomous monoidal category endowed with the choice of an autonomous structure and an isomorphism of monoidal functors between the associated left and right duality functors. In this paper we define and study the algebraic counterpart of sovereign monoidal categories: cosovereign Hopf algebras. We describe the universal cosovereign Hopf algebras, we study finite-dimensional cosovereign Hopf algebras via the dimension theory provided by the sovereign structure and we examine an example generalizing the quantum groups SL q .


Glasgow Mathematical Journal | 2010

HOPF IMAGES AND INNER FAITHFUL REPRESENTATIONS

Teodor Banica; Julien Bichon

We develop a general theory of Hopf image of a Hopf algebra representation, with the associated concept of inner faithful representation, modelled on the notion of faithful representation of a discrete group. We study several examples, including group algebras, enveloping algebras of Lie algebras, pointed Hopf algebras, function algebras, twistings and cotwistings, and we present a Tannaka duality formulation of the notion of Hopf image.


Asian-european Journal of Mathematics | 2008

ALGEBRAIC QUANTUM PERMUTATION GROUPS

Julien Bichon

We discuss some algebraic aspects of quantum permutation groups, working over arbitrary fields. If


Journal of The Institute of Mathematics of Jussieu | 2007

Free product formulae for quantum permutation groups

Teodor Banica; Julien Bichon

K


Journal of Algebra | 2003

Hopf–Galois systems

Julien Bichon

is any characteristic zero field, we show that there exists a universal cosemisimple Hopf algebra coacting on the diagonal algebra


Journal of Algebra and Its Applications | 2006

GALOIS AND BIGALOIS OBJECTS OVER MONOMIAL NON-SEMISIMPLE HOPF ALGEBRAS

Julien Bichon

K^n

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Teodor Banica

Cergy-Pontoise University

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Stephen Curran

University of California

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Sonia Natale

National University of Cordoba

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Simon Riche

Blaise Pascal University

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