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The combinatorics of an algebraic class of easy quantum groups

机译：易量子群的代数类的组合

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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 Sn and the orthogonal group O_n as well as Wang's quantum permutation group S_n~+ and his free orthogonal quantum group O_n~+. In this paper, 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 paper.
机译：易量子群是紧致的矩阵量子群，其相互缠结的空间由分区类别的组合给出。此类包含对称组Sn和正交组O_n以及Wang的量子排列组S_n〜+和他的自由正交量子组O_n〜+。在本文中，我们研究了一类特定的分区类别，为每个分区分配了一个二阶循环组的无限自由积的子组。这是所有易量子基团分类的重要一步，我们推论出其中有无数个。我们专注于这种分配的组合方面，补充了另一篇论文中提出的量子代数观点。

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