Free wreath product quantum groups and standard invariants of subfactors

Representations of compact quantum groups and subfactors

We associate Popa systems (= standard invariants of subfactors, cf. [P3],[P4]) to the finite dimensional representations of compact quantum groups. We characterise the systems arising in this way: these are the ones which can be “represented” on finite dimensional Hilbert spaces. This is proved by an universal construction. We explicitely compute (in terms of some free products) the operation o...

Free Wreath Product by the Quantum Permutation Group

Let A be a compact quantum group, let n ∈ N∗ and let Aaut(Xn) be the quantum permutation group on n letters. A free wreath product construction A∗wAaut(Xn) is done. This construction provides new examples of quantum groups, and is useful to describe the quantum automorphism group of the n-times disjoint union of a finite connected graph.

Automorphism Groups of Wreath Product Digraphs

We strengthen a classical result of Sabidussi giving a necessary and sufficient condition on two graphs, X and Y , for the automorphsim group of the wreath product of the graphs, Aut(X o Y ) to be the wreath product of the automorphism groups Aut(X) o Aut(Y ). We also generalize this to arrive at a similar condition on color digraphs. The main purpose of this paper is to revisit a well-known an...

Automorphisms of Regular Wreath Product p-Groups

We present a useful new characterization of the automorphisms of the regular wreath product group P of a finite cyclic p-group by a finite cyclic p-group, for any prime p, and we discuss an application. We also present a short new proof, based on representation theory, for determining the order of the automorphism group Aut P , where P is the regular wreath product of a finite cyclic p-group by...

Image Processing with Wreath Product Groups