Contractive idempotents on locally compact quantum groups

TL;DR

This paper generalizes Greenleaf's classical results by characterizing contractive idempotent functionals on coamenable locally compact quantum groups, linking them to ternary rings of operators.

Contribution

It provides a new general form for contractive idempotent functionals on quantum groups and establishes a correspondence with ternary rings of operators.

Findings

The image of convolution operators from these functionals forms a ternary ring of operators.

A one-to-one correspondence between contractive idempotents and certain ternary rings of operators is proven.

The results extend classical group measure theory to the quantum group setting.

Abstract

A general form of contractive idempotent functionals on coamenable locally compact quantum groups is obtained, generalising the result of Greenleaf on contractive measures on locally compact groups. The image of a convolution operator associated to a contractive idempotent is shown to be a ternary ring of operators. As a consequence a one-to-one correspondence between contractive idempotents and a certain class of ternary rings of operators is established.