Higher transitive quantum groups: theory and models
Volume 156 / 2019
Colloquium Mathematicum 156 (2019), 1-14
MSC: Primary 46L65; Secondary 60B15.
DOI: 10.4064/cm7473-3-2018
Published online: 3 December 2018
Abstract
We investigate the notion of $k$-transitivity for the quantum permutation groups $G\subset S_N^+$, with a brief review of the known $k=1,2$ results, and with a study of what happens at $k\geq 3$. We then discuss matrix modelling questions for the algebras $C(G)$, notably by introducing the related notions of double and triple flat matrix model. At the level of examples, our main results concern quantum groups coming from complex Hadamard matrices, and from Weyl matrices.
