Traces in braided categories

✍ Scribed by D. Gurevich; R. Leclercq; P. Saponov

• Book ID: 104343139
• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 242 KB
• Volume: 44
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(02)00076-1

✦ Synopsis

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.