From multiplicative unitaries to quantum groups II

Details From multiplicative unitaries to quantum groups II From multiplicative unitaries to quantum groups II

2007-05-17

arxiv.org/abs/0705.2527v2

J. Funct. Anal. 252 (1) (2007), 42-67

Mathematics

Operator Algebras

19 pages, LaTeX

Scientific paper

It is shown that all important features of a $\mathrm{C}^*$-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.

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