Easy quantum groups form a class of compact matrix quantum groups which are completely
determined by set partitions. They have been defined in 2009 by Banica and Speicher in the …

Abstract Consider a tuple (Y 1,…, Y d) of normal operators in a tracial operator algebra
setting with prescribed sizes of the eigenspaces for each Y i. We address the question what …

We prove several de Finetti theorems for the unitary dual group, also called the Brown
algebra. Firstly, we provide a finite de Finetti theorem characterizing $ R $-diagonal …

We consider the effect of a partial transpose on the limit $* $-distribution of a Haar
distributed random unitary matrix. If we fix, $ b $, the number of blocks, we show that the …

In the present paper, we study some properties of the Heisenberg Lie algebra of dimension.
The main purpose of this research is to construct a real Frobenius Lie algebra from the …

In this note, we study the asymptotic properties of the⁎-distribution of traces of some
matrices, with respect to the free Haar trace on the unitary dual group. The considered …

We generalize the result of block-wise convergence of the Brownian motion on the unitary
group $ U (nm) $ towards a quantum L\'evy process on the unitary dual group $ U\langle …

Dans une première partie, nous introduisons les outils des mathématiques non
commutatives que nous utiliserons dans notre étude des groupes quantiques finis et des …

Noncommutative Mathematics are a very active domain. The idea underlying it is that
instead of describing a space as a set of points, it is equivalent to describe it with the algebra …

This thesis is devoted to the study of two quite different questions, which are related by the
tools that we use to study them. The first question is that of the definition of lattice gauge …