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On non-semisimple fusion rules and tensor categories
Karlstad University, Faculty of Technology and Science, Department of Physics and Electrical Engineering.ORCID iD: 0000-0003-4081-6234
2007 (English)In: Contemporary Mathematics 442 (2007), 2007Chapter in book (Refereed)
Abstract [en]

Category theoretic aspects of non-rational conformal field theories are discussed. We consider the case that the category C of chiral sectors is a finite tensor category, i.e. a rigid monoidal category whose class of objects has certain finiteness properties. Besides the simple objects, the indecomposable projective objects of C are of particular interest.

The fusion rules of C can be block-diagonalized. A conjectural connection between the block-diagonalization and modular transformations of characters of modules over vertex algebras is exemplified with the case of the (1,p) minimal models

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URN: urn:nbn:se:kau:diva-22052OAI: diva2:595728
Available from: 2013-01-21 Created: 2013-01-21 Last updated: 2014-11-21

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Fuchs, Jürgen
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