Regular Objects, Multiplicative Unitaries and Conjugation
Abstract
The notion of left (resp. right) regular object of a tensor C*-category equipped with a faithful tensor functor into the category of Hilbert spaces is introduced. If such a category has a left (resp. right) regular object, it can be interpreted as a category of corepresentations (resp. representations) of some multiplicative unitary. A regular object is an object of the category which is at the same time left and right regular in a coherent way. A category with a regular object is endowed with an associated standard braided symmetry. Conjugation is discussed in the context of multiplicative unitaries and their associated Hopf C*-algebras. It is shown that the conjugate of a left regular object is a right regular object in the same category. Furthermore the representation category of a locally compact quantum group has a conjugation. The associated multiplicative unitary is a regular object in that category.
Cite
@article{arxiv.math/0203051,
title = {Regular Objects, Multiplicative Unitaries and Conjugation},
author = {Claudia Pinzari and John E. Roberts},
journal= {arXiv preprint arXiv:math/0203051},
year = {2007}
}
Comments
48 pages, Latex