A note on reduced and von Neumann algebraic free wreath products

@article{Wahl2014ANO,
  title={A note on reduced and von Neumann algebraic free wreath products},
  author={Jonas Wahl},
  journal={arXiv: Operator Algebras},
  year={2014}
}
  • J. Wahl
  • Published 18 November 2014
  • Mathematics
  • arXiv: Operator Algebras
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 quantum group. Based on recent result on their corepresentation theory by Lemeux and Tarrago, we prove that $\mathbb G \wr_* S_N^+$ is of Kac type whenever $\mathbb G$ is, and that the reduced version of $\mathbb G \wr_* S_N^+$ is simple with unique trace state whenever $N \geq 8$. Moreover, we prove… 
Unitary Easy Quantum Groups: the free case and the group case
Easy quantum groups have been studied intensively since the time they were introduced by Banica and Speicher in 2009. They arise as a subclass of ($C^*$-algebraic) compact matrix quantum groups in
Non-commutative generalization of some probabilistic results from representation theory
The subject of this thesis is the non-commutative generalization of some probabilistic results that occur in representation theory. The results of the thesis are divided into three different parts.
Introduction to compact (matrix) quantum groups and Banica–Speicher (easy) quantum groups
This is a transcript of a series of eight lectures, 90 min each, held at IMSc Chennai, India from 5–24 January 2015. We give basic definitions, properties and examples of compact quantum groups and

References

SHOWING 1-10 OF 24 REFERENCES
Haagerup property for quantum reflection groups
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,
Symmetries of a generic coaction
TLDR
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.
Reduced Operator Algebras of Trace-Preserving Quantum Automorphism Groups
Let B be a finite dimensional C ∗ -algebra equipped with its canonical trace induced by the regular representation of B on it- self. In this paper, we study various properties of the trace-preserving
Locally compact quantum groups in the von Neumann algebraic setting
In this paper we complete in several aspects the picture of locally compact quantum groups. First of all we give a definition of a locally compact quantum group in the von Neumann algebraic setting
A Survey of $C^*$-algebraic Quantum Groups, Part I
We develop the nite-dimensional o-representation theory and dis uss the generalized Tannaka-Krein Theorem. The Haar fun tional (whose existen e is one of the major a hievements of Woronowi z's
Approximation properties for free orthogonal and free unitary quantum groups
Abstract In this paper, we study the structure of the reduced C*-algebras and von Neumann algebras associated to the free orthogonal and free unitary quantum groups. We show that the reduced von
Fusion rules for quantum reflection groups
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
A Noncommutative de Finetti Theorem: Invariance under Quantum Permutations is Equivalent to Freeness with Amalgamation
We show that the classical de Finetti theorem has a canonical noncommutative counterpart if we strengthen “exchangeability” (i.e., invariance of the joint distribution of the random variables under
The boundary of universal discrete quantum groups, exactness, and factoriality
We study the C -algebras and von Neumann algebras associated with the universal discrete quantum groups. They give rise to full prime factors and simple exact C -algebras. The main tool in our work
...
...