The combinatorics of an algebraic class of easy quantum groups
Abstract
Easy quantum groups are compact matrix quantum groups, whose intertwiner spaces are given by the combinatorics of categories of partitions. This class contains the symmetric group and the orthogonal group as well as Wang's quantum permutation group and his free orthogonal quantum group. In this article, we study a particular class of categories of partitions to each of which we assign a subgroup of the infinite free product of the cyclic group of order two. This is an important step in the classification of all easy quantum groups and we deduce that there are uncountably many of them. We focus on the combinatorial aspects of this assignment, complementing the quantum algebraic point of view presented in another article.
Cite
@article{arxiv.1312.1497,
title = {The combinatorics of an algebraic class of easy quantum groups},
author = {Sven Raum and Moritz Weber},
journal= {arXiv preprint arXiv:1312.1497},
year = {2013}
}
Comments
16 pages; This article contains the combinatorial essence of arXiv:1212.4742v1. For a substantially extended and broadened version of arXiv:1212.4742v1 which makes use of quantum group theory, see arXiv:1311.7630v1