Year: 2014
Type: preprint
Abstract: We generalise the notions of semi-regularity, regularity, and bi-regularity to unitary solutions of the braided Pentagon equation in concrete W*-categories with semi-regular/regular/bi-regular braiding, and study their properties. We show, for example, that under bi-regularity-assumptions, the leg-algebras form braided C*-bialgebras. Moreover, we "close the circle" for the representation categories: The braiding on the Yetter-Drinfeld category of a (semi-)regular multiplicative unitary in a category with (semi-)regular braiding is again (semi-)regular.
Source: arXiv (Cornell University)
Authors: Buecher, David, Roy, Sutanu
Institutions: Indian Statistical Institute, University of Göttingen
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W2274379722