自相似量子群

摘要：

引入紧量子群的自相似性概念。对于有限集$X$，我们引入了一个$C^*$ -代数$\mathbb{A}_X$，它是无限齐次有根树$X^*$的量子自同构群.自相似量子群则是$\mathbb{A}_X$的某些量子子群。我们的主要类别的例子被称为有限约束的自相似量子群，我们发现一类这样的例子，可以被描述为量子置换群的子群的量子圈积。

英文摘要：

We introduce the notion of self-similarity for compact quantum groups. For a finite set $X$, we introduce a $C^*$-algebra $\mathbb{A}_X$, which is the quantum automorphism group of the infinite homogeneous rooted tree $X^*$. Self-similar quantum groups are then certain quantum subgroups of $\mathbb{A}_X$. Our main class of examples are called finitely-constrained self-similar quantum groups, and we find a class of these examples that can be described as quantum wreath products by subgroups of the quantum permutation group.

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