Isometric coactions of compact quantum groups on compact quantum metric spaces

TL;DR

This paper introduces a concept of isometric coactions of compact quantum groups on quantum metric spaces, establishing the existence of a quantum isometry group that preserves the metric and a specified state.

Contribution

It defines isometric coactions in the quantum setting and proves the existence of quantum isometry groups for finite metric quantum spaces.

Findings

Existence of quantum isometry groups for finite metric quantum spaces

Definition of isometric coactions in the quantum context

Preservation of a given state by the quantum isometry group

Abstract

We propose a notion of isometric coaction of a compact quantum group on a compact quantum metric space in the framework of Rieffel where the metric structure is given by a Lipnorm. We prove the existence of a quantum isometry group for finite metric quantum spaces, preserving a given state.