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.
Keywords
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}
}
Comments
23 pages