Weight theory for C*-algebraic quantum groups

TL;DR

This paper develops technical results on weights in C*-algebras, facilitating the study of locally compact quantum groups within the C*-algebra framework.

Contribution

It introduces new methods for extending weights, analyzes slice weights and tensor products, and supports the theory of locally compact quantum groups in C*-algebras.

Findings

Extension of lower semi-continuous weights to normal weights

Analysis of slice weights and their KSGNS-constructions

Tensor product of weights with partial GNS-construction

Abstract

In this paper, we collect some technical results about weights on C*-algebras which are useful in de theory of locally compact quantum groups in the C*-algebra framework. We discuss the extension of a lower semi-continuous weight to a normal weight following S. Baaj, look into slice weights and their KSGNS-constructions and investigate the tensor product of weights together with a partial GNS-construction for such a tensor product. This paper accompanies our paper 'Locally compact quantum groups' in which we propose a relatively simple definition of a locally compact quantum group in the C*-algebra framework.