Haar measure on a locally compact quantum group

Abstract

In the general theory of locally compact quantum groups, the notion of Haar measure (Haar weight) plays the most significant role. The aim of this paper is to carry out a careful analysis regarding Haar weight, in relation to general theory, for the specific non-compact quantum group (A,Δ) constructed earlier by the author. In this way, one can show that (A,Δ) is indeed a ``(C*-algebraic) locally compact quantum group'' in the sense of the recently developed definition given by Kustermans and Vaes. Attention will be given to pointing out the relationship between the original construction (obtained by deformation quantization) and the structure maps suggested by general theory.