Traces in braided categories
Abstract
With any even Hecke symmetry R (that is a Hecke type solution of the Yang-Baxter equation) we associate a quasitensor category. We formulate a condition on R implying that the constructed category is rigid and its commutativity isomorphisms R_{U,V} are natural. We show that this condition leads to rescaling of the initial Hecke symmetry. We suggest a new way of introducing traces as properly normalized categorical morphisms End(V) --> K and deduce the corresponding normalization from categorical dimensions.
Cite
@article{arxiv.math/0104202,
title = {Traces in braided categories},
author = {D. Gurevich and R. Leclercq and P. Saponov},
journal= {arXiv preprint arXiv:math/0104202},
year = {2009}
}
Comments
Source: Revised version, a more attention is given to the problem of trace definition and its proper normalization in braided categories with Hecke type braidings. Minor corrections in Introduction. LaTex file, all macros included, no figures