On non-semisimple fusion rules and tensor categories

Jurgen Fuchs

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arXiv · hep-th/0602051

On non-semisimple fusion rules and tensor categories

Jurgen Fuchs

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Abstract

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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Jurgen Fuchs. 2006-02-06. On non-semisimple fusion rules and tensor categories. https://arxiv.org/abs/hep-th/0602051

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