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Category theory for conformal boundary conditions
Karlstad University, Faculty of Technology and Science, Department of Physics and Electrical Engineering.ORCID iD: 0000-0003-4081-6234
2003 (English)In: Fields Institute Communications 39 (2003), 2003Chapter in book (Refereed)
Abstract [en]

We study properties of the category of modules of an algebra object A in a tensor category C. We show that the module category inherits various structures from C, provided that A is a Frobenius algebra with certain additional properties. As a by-product we obtain results about the Frobenius-Schur indicator in sovereign tensor categories. A braiding on C is not needed, nor is semisimplicity.



We apply our results to the description of boundary conditions in two-dimensional conformal field theory and present illustrative examples. We show that when the module category is tensor, then it gives rise to a NIM-rep of the fusion rules, and discuss a possible relation with the representation theory of vertex

operator algebras

Place, publisher, year, edition, pages
2003.
National Category
Physical Sciences
Research subject
Physics
Identifiers
URN: urn:nbn:se:kau:diva-17593OAI: oai:DiVA.org:kau-17593DiVA: diva2:591201
Available from: 2013-01-21 Created: 2013-01-21 Last updated: 2014-11-21

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http://www.ams.org/bookstore?fn=20&arg1=ficseries&item=FIC-39http://xxx.lanl.gov/abs/math/0106050

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Fuchs, Jürgen
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