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Braided Tensor Categories of Admissible Modules for Affine Lie Algebras

  • Thomas Creutzig
  • Yi-Zhi Huang
  • Jinwei Yang
Article
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Abstract

Using the tensor category theory developed by Lepowsky, Zhang and the second author, we construct a braided tensor category structure with a twist on a semisimple category of modules for an affine Lie algebra at an admissible level. We conjecture that this braided tensor category is rigid and thus is a ribbon category. We also give conjectures on the modularity of this category and on the equivalence with a suitable quantum group tensor category. In the special case that the affine Lie algebra is \({\widehat{\mathfrak{sl}}_2}\), we prove the rigidity and modularity conjectures.

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Notes

Acknowledgements

T. C. is supported by the Natural Sciences and Engineering Research Council of Canada (RES0020460). J. Y. is supported in part by an AMS-Simons travel Grant. J. Y. also wants to thank Zongzhu Lin for useful conversations.

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Authors and Affiliations

  1. 1.Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada
  2. 2.Department of MathematicsRutgers UniversityPiscatawayUSA
  3. 3.Department of MathematicsYale UniversityNew HavenUSA

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