Free Wreath Product by the Quantum Permutation Group

By Julien Bichon. 2001

120 citations recorded by the source corpus.

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 introduced. 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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/524342c3ae266dd5a5a0e4b9df954047ec6c1a65

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Citations in the corpus

The Haagerup property for locally compact quantum groups (2013, background): “The duals of the free orthogonal quantum groups, of the free unitary quantum groups, of the quantum automorphism groups of certain finite-dimensional C -algebras equipped with canonical traces, and of the quantum reflection groups H sC n (the free wreath products Zs o S n , see [9]) for n 4 and 1 s ”
Unitary Easy Quantum Groups: the free case and the group case (2015, methodology): “ith the whole C∗-algebra, so the question of how to endow the C∗-algebra in the above deﬁnition with a compact matrix quantum group structure lies only in the deﬁnition of the generating unitary. See [Bic04] for a proof that the free wreath product is a compact matrix quantum group. 4.5. Constructio”
Quantum permutation groups: a survey (2006, background): “This notion, introduced in [20], is justified by formulae of the following type, where G,A denote classical symmetry groups, respectively quantum symmetry algebras:”
Quantum automorphism groups of homogeneous graphs (2003, background): “Indeed, the algebra associated in [3] to a finite metric space Y is the same as the algebra H(Ygr), where Ygr is the complete graph having vertices at points of Y , with edges colored by corresponding lengths.”