On free actions of discrete quantum groups

TL;DR

This paper extends a classical result by Ellis to discrete quantum groups with low duals, demonstrating their free actions on their Stone-Cech compactification using noncommutative geometry techniques.

Contribution

It introduces a novel proof method for free actions of discrete quantum groups, expanding classical results into the quantum setting.

Findings

Discrete quantum groups with low duals act freely on their Stone-Cech compactification.

The proof employs noncommutative geometry, differing from classical approaches.

The result generalizes classical group actions to the quantum context.

Abstract

R. Ellis showed in 1960 that every discrete group acts freely on its Stone-Cech compactification. We extend this result to discrete quantum groups with low duals. The method of proof is different from the earlier proofs in the classical case, using the definition of freeness given by D. A. Ellwood in the setting of noncommutative geometry.