Regular Objects, Multiplicative Unitaries and Conjugation

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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.
48 pages, Latex

Keywords

Operator Algebras, 81R50, 18D10

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/63500

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0203051
 http://arxiv.org/abs/math/0203051

Collections

arXiv