Self-similar quantum groups

Abstract

<p>We introduce the notion of self-similarity for compact quantum groups. For a finite set <i>X</i>, we introduce a <i>C*</i> -algebra A<i>_X</i>, which is the quantum automorphism group of the infinite homogeneous rooted tree <i>X*</i>. Self-similar quantum groups are then certain quantum subgroups of A<i>_X</i>. 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.</p>