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From multiplicative unitaries to quantum groups. (English) Zbl 0876.46044
Author’s summary: An alternative version of the theory of multiplicative unitaries is presented. Instead of the original regularity condition of S. Baaj and G. Skandalis [Ann. Sci. Éc. Norm. Supér., IV. Sér. 26, 425-488 (1993; Zbl 0804.46078)] we formulate another condition selecting manageable multiplicative unitaries. The manageability is the property of multiplicative unitaries coming from the quantum group theory. For manageable multiplicative unitaries we reproduce all the essential results of the original paper of Baaj and Skandalis and much more. In particular the existence of the antipode and its polar decomposition is shown.
Reviewer: M.Masmoudi (Metz)

MSC:
46L55 Noncommutative dynamical systems
17B37 Quantum groups (quantized enveloping algebras) and related deformations
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