We introduce a notion of quantum function and develop a compositional framework for finite
quantum set theory based on a 2-category of quantum sets and quantum functions. We use …

We investigate the fundamental concept of a closed quantum subgroup of a locally compact
quantum group. Two definitions—one due to S. Vaes and one due to SL Woronowicz—are …

This is a presentation of recent work on quantum permutation groups. Contains: a short
introduction to operator algebras and Hopf algebras; quantum permutation groups, and their …

We classify instances of quantum pseudo-telepathy in the graph isomorphism game,
exploiting the recently discovered connection between quantum information and the theory …

We develop a general theory of Hopf image of a Hopf algebra representation, with the
associated concept of inner faithful representation, modelled on the notion of faithful …

An organised step-by-step introduction to the theory of compact quantum groups, starting
with examples coming from quantum physics, which stems from the basic undergraduate …

Let B be a finite dimensional C∗-algebra equipped with its canonical trace induced by the
regular representation of B on itself. In this paper, we study various properties of the trace …

The concept of quantum automorphism groups of finite graphs was introduced by Banica
and Bichon in [1, 9]. It generalizes the classical automorphism groups of graphs within the …

We classify quantum analogues of actions of finite subgroups G of SL 2⁢(k) on commutative
polynomial rings k⁢[u, v]. More precisely, we produce a classification of pairs (H, R) where H …

We study the matrix models π: C (S N+)→ MN (C (X)) which are flat, in the sense that the
standard generators of C (S N+) are mapped to rank 1 projections. Our first result is a …