From multiplicative unitaries to quantum groups II

Abstract

It is shown that all important features of a ${\mathrm{C}}^{\ast }$-algebraic quantum group $(A,\Delta )$ defined by a modular multiplicative $W$ depend only on the pair $(A,\Delta )$ rather than the multiplicative unitary operator $W$. The proof is based on thorough study of representations of quantum groups. As an application we present a construction and study properties of the universal dual of a quantum group defined by a modular multiplicative unitary - without assuming existence of Haar weights.

arXiv comment19 pages, LaTeX