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Traces in non-semisimple categories

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OAS - Operator algebras: subfactors and their applications

Quite generally, a trace on a k-linear category is a family of functions from the endomorphisms of objects to the underlying field k, subject to cyclicity and possibly other constraints. In some interesting cases these functions may only exist for a subset of all objects. One situation where this may happen are non-semisimple braided finite tensor categories, which have applications in link invariants and in two-dimensional conformal field theory. In this talk I will present some results and conjectures related to such categories.





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