We define quantum automorphisms and isomorphisms of Hadamard matrices. We show that
every Hadamard matrix of size $ N\ge 4$ has quantum symmetries and that all Hadamard …

We present an algorithm for approximating linear categories of partitions (of sets). We report
on concrete computer experiments based on this algorithm which we used to obtain first …

We classify extremal traces on the seven direct limit algebras of noncrossing partitions
arising from the classification of free partition quantum groups of Banica–Speicher 5 and …

We define the quantum group D 4+–a free quantum version of the demihyperoctahedral
group D 4 (the smallest representative of the Coxeter series D). In order to do so, we …

One key result obtained from the investigation of compact matrix quantum groups is a
Tannaka-Krein type duality, by which any compact matrix quantum group can be fully …

In continuation of our recent work arXiv: 2006.07312, we classify the extremal traces on
infinite diagram algebras that appear in the context of Schur-Weyl duality for Banica and …

Compact quantum groups can be found by solving certain combinatorics problems, as first
shown by Banica and Speicher. Any system of partitions of finite sets which is closed under …

This is a survey on some results obtained recently in the classification of compact quantum
groups associated to partitions, with a focus on the non-crossing case. We take a global look …

In continuation of our recent work [39], we classify the extremal traces on infinite diagram
algebras that appear in the context of Schur–Weyl duality for Banica and Speicher's easy …