# Free wreath product quantum groups : the monoidal category, approximation properties and free probability

@article{Lemeux2014FreeWP, title={Free wreath product quantum groups : the monoidal category, approximation properties and free probability}, author={Franccois Lemeux and Pierre Tarrago}, journal={arXiv: Quantum Algebra}, year={2014} }

## 30 Citations

### Free wreath product quantum groups and standard invariants of subfactors

- MathematicsAdvances in Mathematics
- 2018

### A note on reduced and von Neumann algebraic free wreath products

- Mathematics
- 2014

In this paper, we study operator algebraic properties of the reduced and von Neumann algebraic versions of the free wreath products $\mathbb G \wr_* S_N^+$, where $\mathbb G$ is a compact matrix…

### Torsion and K-theory for some free wreath products

- Mathematics
- 2017

We classify torsion actions of free wreath products of arbitrary compact quantum groups and use this to prove that if $\mathbb{G}$ is a torsion-free compact quantum group satisfying the strong…

### Maximal torus theory for compact quantum groups

- Mathematics
- 2016

Associated to any compact quantum group $G\subset U_N^+$ is a canonical family of group dual subgroups $\widehat{\Gamma}_Q\subset G$, parametrized by unitaries $Q\in U_N$, playing the role of…

### RIESZ TRANSFORMS ON COMPACT QUANTUM GROUPS AND STRONG SOLIDITY

- MathematicsJournal of the Institute of Mathematics of Jussieu
- 2021

Abstract One of the main aims of this paper is to give a large class of strongly solid compact quantum groups. We do this by using quantum Markov semigroups and noncommutative Riesz transforms. We…

### Traces on diagram algebras I: Free partition quantum groups, random lattice paths and random walks on trees

- MathematicsJournal of the London Mathematical Society
- 2022

We classify extremal traces on the seven direct limit algebras of noncrossing partitions arising from the classification of free partition quantum groups of Banica–Speicher [5] and Weber [42]. For…

### Super-easy quantum groups with arbitrary parameters

- Mathematics
- 2018

We discuss an extended easy quantum group formalism, with the Schur-Weyl theoretic Kronecker symbols being as general as possible, and allowed to take values in $\{-1,0,1\}$, and more generally in…

### Monoidal Rigidity for Free Wreath Products

- Mathematics
- 2016

In this note we observe that any compact quantum group monoidally equivalent, in a nice way, to a free wreath product of a compact quantum group $G$ by the quantum automorphism group of a finite…

### ON THE PARTITION APPROACH TO SCHUR-WEYL DUALITY AND FREE QUANTUM GROUPS

- Mathematics
- 2014

We give a general definition of classical and quantum groups whose representation theory is “determined by partitions” and study their structure. This encompasses many examples of classical groups…

## References

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- 2014

In this paper, we study operator algebraic properties of the reduced and von Neumann algebraic versions of the free wreath products $\mathbb G \wr_* S_N^+$, where $\mathbb G$ is a compact matrix…

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In this paper we prove that the duals of the quantum reflection groups have the Haagerup property for all $N\ge4$ and $s\in[1,\infty)$. We use the canonical arrow onto the quantum permutation groups,…

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Compact matrix quantum groups are strongly determined by their intertwiner spaces, due to a result by S.L. Woronowicz. In the case of easy quantum groups, the intertwiner spaces are given by the…

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We find the fusion rules for the quantum analogues of the complex reflection groups $H_n^s=\mathbb Z_s\wr S_n$. The irreducible representations can be indexed by the elements of the free monoid…

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Abstract We introduce and study a remarkable family of real probability measures ${{\pi }_{st}}$ that we call free Bessel laws. These are related to the free Poisson law $\pi $ via the formulae…

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The Haagerup property for locally compact groups is generalised to the context of locally compact quantum groups, with several equivalent characterisations in terms of the unitary representations and…