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Traces in braided categories

D. Gurevich·R. Leclercq·P. Saponov
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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.

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D. Gurevich, R. Leclercq, P. Saponov. 2002-04-24. Traces in braided categories. https://doi.org/10.1016/s0393-0440(02)00076-1

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