English

On non-semisimple fusion rules and tensor categories

High Energy Physics - Theory 2007-05-23 v1 Category Theory Quantum Algebra

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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Cite

@article{arxiv.hep-th/0602051,
  title  = {On non-semisimple fusion rules and tensor categories},
  author = {Jurgen Fuchs},
  journal= {arXiv preprint arXiv:hep-th/0602051},
  year   = {2007}
}

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23 pages