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 in the sense of [20]. We show that this condition leads to rescaling 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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