Traces in braided categories

Details Traces in braided categories Traces in braided categories

2001-04-20

arxiv.org/abs/math/0104202v3

Mathematics

Quantum Algebra

Source: Revised version, a more attention is given to the problem of trace definition and its proper normalization in braided

Scientific paper

10.1016/S0393-0440(02)00076-1

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.

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