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
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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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Monoidal Rigidity for Free Wreath Products
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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…
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References
SHOWING 1-10 OF 60 REFERENCES
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…
Asymptotic Infinitesimal Freeness with Amalgamation for Haar Quantum Unitary Random Matrices
- Mathematics
- 2009
We consider the limiting distribution of $${U_NA_NU_N^*}$$ and BN (and more general expressions), where AN and BN are N × N matrices with entries in a unital C*-algebra $${\mathcal B}$$ which have…
Symmetries of a generic coaction
- Mathematics, Computer Science
- 1998
A structure result is obtained for G_{aut}(\widehat{B}) in the case where B is a matrix algebra and the fixed point subfactor of P has index n and principal graph A_\infty.
Haagerup property for quantum reflection groups
- Mathematics
- 2013
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,…
On the representation theory of partition (easy) quantum groups
- Mathematics
- 2013
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…
Fusion rules for quantum reflection groups
- Mathematics
- 2008
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…
Free Bessel Laws
- MathematicsCanadian Journal of Mathematics
- 2011
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…
The Haagerup property for locally compact quantum groups
- Mathematics
- 2013
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…