We propose a definition of partition quantum spaces. They are given by universal $C*$-algebras whose relations come from partitions of sets. We ask for the maximal compact matrix quantum group acting on them. We show how those fit into the setting of easy quantum groups: Our approach yields spaces these groups are acting on. In a way, our partition quantum spaces arise as the first d columns of easy quantum groups. However, we define them as universal $C*$-algebras rather than as $C*$-subalgebras of easy quantum groups. We also investigate the minimal number $d$ needed to recover an easy quantum group as the quantum symmetry group of a partition quantum space. In the free unitary case, d takes the values one or two.

中文翻译：

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分区量子空间

我们提出了一个划分量子空间的定义。它们由通用的$ C * $代数给出，它们的关系来自集合的分区。我们要求作用在它们上的最大紧致矩阵量子组。我们展示了它们如何适合于简单量子组的设置：我们的方法产生了这些组所作用的空间。在某种程度上，我们的分配量子空间是易量子基团的前d列。但是，我们将它们定义为通用$ C * $-代数，而不是简单量子组的$ C * $-子代数。我们还研究了恢复一个容易的量子组作为分区量子空间的量子对称组所需的最小数量$ d $。在自由unit的情况下，d取值一或二。