Harmonic Operators of Ergodic Quantum Group Actions

TL;DR

This paper investigates harmonic elements arising from ergodic quantum group actions on von Neumann algebras, providing conditions for their triviality, thus advancing understanding of quantum symmetries in operator algebras.

Contribution

It introduces new equivalent conditions characterizing when harmonic elements are trivial in the context of ergodic quantum group actions.

Findings

Identifies conditions for trivial harmonic elements

Establishes equivalences related to ergodic actions

Enhances understanding of quantum symmetries in operator algebras

Abstract

In this paper we study the harmonic elements of (convolution) Markov maps associated to (ergodic) actions of locally compact quantum groups on ($\sigma$-finite) von Neumann algebras. We give several equivalent conditions under which the harmonic elements are trivial.