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Module categories for permutation modular invariants
Karlstad University, Faculty of Technology and Science, Department of Physics and Electrical Engineering. (Matematisk modellering)ORCID iD: 0000-0003-4081-6234
2010 (English)In: International mathematics research notices, ISSN 1073-7928, Vol. 2010, no 16, 3067-3100 p.Article in journal (Refereed) Published
Abstract [en]

We show that a braided monoidal category C can be endowed with the structure of a right (and left) module category over C \times C. In fact, there is a family of such module category structures, and they are mutually isomorphic if and only if C allows for a twist. For the case that C is premodular, we compute the internal End of the tensor unit of C, and we show that it is an Azumaya algebra if C is modular. As an application to two-dimensional rational conformal field theory, we show that the module categories describe the permutation modular invariant for models based on the product of two identical chiral algebras. It follows in particular that all permutation modular invariants are physical

Place, publisher, year, edition, pages
2010. Vol. 2010, no 16, 3067-3100 p.
National Category
Physical Sciences
Research subject
Physics
Identifiers
URN: urn:nbn:se:kau:diva-9833DOI: 10.1093/imrn/rnp235OAI: oai:DiVA.org:kau-9833DiVA: diva2:493340
Available from: 2012-02-08 Created: 2012-02-08 Last updated: 2015-06-25Bibliographically approved

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Publisher's full texthttp://dx.doi.org/10.1515/CRELLE.2010.035

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