Idempotent states on locally compact quantum groups II

TL;DR

This paper extends the correspondence between idempotent states and invariant subalgebras to a broader class of locally compact quantum groups, demonstrating automatic preservation of Haar weight by convolution operators.

Contribution

It generalizes the theory to non-coamenable, non-unimodular quantum groups, expanding understanding of their algebraic structures.

Findings

Extended the correspondence to non-coamenable, non-unimodular groups

Showed convolution operators preserve the right Haar weight

Broadened the theoretical framework of quantum group analysis

Abstract

Correspondence between idempotent states and expected right-invariant subalgebras is extended to non-coamenable, non-unimodular locally compact quantum groups; in particular left convolution operators are shown to automatically preserve the right Haar weight.