Regular Objects and Multiplicative Unitaries
by
J.E. Roberts
Università di Roma Tor Vergata
Coauthors: C. Pinzari

The talk provides a new interpretation of multiplicative unitaries in terms of regular objects of a tensor C^*-category equipped with a faithful tensor functor into the category of Hilbert space. If such a category has a regular object, it can be interpreted as the category of representations of a multiplicative unitary, and, at the same time, as a category of corepresentations of some other multiplicative unitary. Furthermore, the category is endowed with an associated standard braided symmetry.

Conjugation will be discussed, in the context of multiplicative unitaries and the associated Hopf C^*-algebras. Multiplicative unitaries arising from locally compact quantum groups in the sense of Masuda, Nakagami and Woronowicz are left regular objects in their corepresentation category, and have a canonical conjugate which is a right regular object of the same category.

Date received: June 15, 2000